constant group bound verified_certificate evidence source literature_latex literature_decimal_approx literature_alt_display verified_latex verified_decimal_approx verified_alt_display ramsey-3-4 ramsey upper lean greenwood-gleason-1955 9 9.0 ramsey-3-5 ramsey upper lean greenwood-gleason-1955 14 14.0 ramsey-3-6 ramsey upper lean kery-1964 18 18.0 ramsey-3-7 ramsey upper lean graver-yackel-1968 23 23.0 ramsey-3-8 ramsey upper lean mckay-zhang-1992 28 28.0 ramsey-3-9 ramsey upper lean grinstead-roberts-1982 36 36.0 ramsey-3-10 ramsey lower ramsey-3-10-lower-39 witness exoo-1989c 40 40.0 39 39.0 ramsey-3-10 ramsey upper lean angeltveit-2024 41 41.0 ramsey-3-11 ramsey lower ramsey-3-11-lower-46 witness exoo-2013 47 47.0 46 46.0 ramsey-3-11 ramsey upper lean goedgebeur-radziszowski-2013 50 50.0 ramsey-3-12 ramsey lower ramsey-3-12-lower-49 witness kolodyazhny-2015 53 53.0 49 49.0 ramsey-3-12 ramsey upper lean lesser-2001 59 59.0 ramsey-3-13 ramsey lower ramsey-3-13-lower-58 witness nagda-raghavan-thakurta-2026 61 61.0 58 58.0 ramsey-3-13 ramsey upper lean goedgebeur-radziszowski-2013 68 68.0 ramsey-3-14 ramsey lower ramsey-3-14-lower-64 witness kolodyazhny-2016 67 67.0 64 64.0 ramsey-3-14 ramsey upper lean goedgebeur-radziszowski-2013 77 77.0 ramsey-3-15 ramsey lower ramsey-3-15-lower-72 witness kolodyazhny-2016 74 74.0 72 72.0 ramsey-3-15 ramsey upper lean goedgebeur-radziszowski-2013 87 87.0 ramsey-4-4 ramsey upper lean greenwood-gleason-1955 18 18.0 ramsey-4-5 ramsey upper lean mckay-radziszowski-1995 25 25.0 ramsey-4-6 ramsey lower ramsey-4-6-lower-34 witness exoo-2012 36 36.0 34 34.0 ramsey-4-6 ramsey upper lean angeltveit-mckay-2019-2024 40 40.0 ramsey-4-7 ramsey lower ramsey-4-7-lower-47 witness exoo-1989a 49 49.0 47 47.0 ramsey-4-7 ramsey upper lean angeltveit-mckay-2019-2024 58 58.0 ramsey-4-8 ramsey lower ramsey-4-8-lower-52 witness exoo-tatarevic-2015 59 59.0 52 52.0 ramsey-4-8 ramsey upper lean angeltveit-mckay-2019-2024 79 79.0 ramsey-4-9 ramsey lower ramsey-4-9-lower-69 witness exoo-2005 73 73.0 69 69.0 ramsey-4-9 ramsey upper lean angeltveit-mckay-2019-2024 105 105.0 ramsey-4-10 ramsey lower witness harborth-krause-2003 92 92.0 ramsey-4-10 ramsey upper lean angeltveit-mckay-2019-2024 135 135.0 ramsey-4-11 ramsey lower witness exoo-tatarevic-2015 102 102.0 ramsey-4-11 ramsey upper lean angeltveit-mckay-2019-2024 170 170.0 ramsey-4-12 ramsey lower witness su-luo-li-1998 128 128.0 ramsey-4-12 ramsey upper lean angeltveit-mckay-2019-2024 210 210.0 ramsey-4-13 ramsey lower witness nagda-raghavan-thakurta-2026 139 139.0 ramsey-4-13 ramsey upper lean angeltveit-mckay-2019-2024 256 256.0 ramsey-4-14 ramsey lower witness nagda-raghavan-thakurta-2026 148 148.0 ramsey-4-14 ramsey upper lean angeltveit-mckay-2019-2024 307 307.0 ramsey-4-15 ramsey lower witness nagda-raghavan-thakurta-2026 159 159.0 ramsey-4-15 ramsey upper lean angeltveit-mckay-2019-2024 364 364.0 ramsey-5-5 ramsey lower ramsey-5-5-lower-42 witness exoo-1989b 43 43.0 42 42.0 ramsey-5-5 ramsey upper lean angeltveit-mckay-2024 46 46.0 ramsey-5-6 ramsey lower ramsey-5-6-lower-54 witness exoo-2023 59 59.0 54 54.0 ramsey-5-6 ramsey upper lean angeltveit-mckay-2019-2024 85 85.0 ramsey-5-7 ramsey lower ramsey-5-7-lower-71 witness calkin-erdos-tovey-1997 80 80.0 71 71.0 ramsey-5-7 ramsey upper lean angeltveit-mckay-2019-2024 133 133.0 ramsey-5-8 ramsey lower witness harborth-krause-2003 101 101.0 ramsey-5-8 ramsey upper lean angeltveit-mckay-2019-2024 193 193.0 ramsey-5-9 ramsey lower witness kuznetsov-2016 133 133.0 ramsey-5-9 ramsey upper lean angeltveit-mckay-2019-2024 282 282.0 ramsey-5-10 ramsey lower witness exoo-tatarevic-2015 149 149.0 ramsey-5-10 ramsey upper lean angeltveit-mckay-2019-2024 381 381.0 ramsey-5-11 ramsey lower witness kuznetsov-2016 183 183.0 ramsey-5-11 ramsey upper lean angeltveit-mckay-2019-2024 511 511.0 ramsey-5-12 ramsey lower witness kuznetsov-2016 203 203.0 ramsey-5-12 ramsey upper lean angeltveit-mckay-2019-2024 672 672.0 ramsey-5-13 ramsey lower witness kuznetsov-2016 233 233.0 ramsey-5-13 ramsey upper lean angeltveit-mckay-2019-2024 860 860.0 ramsey-5-14 ramsey lower witness kuznetsov-2016 267 267.0 ramsey-5-14 ramsey upper lean angeltveit-mckay-2019-2024 1081 1081.0 ramsey-5-15 ramsey lower witness trivial 275 275.0 ramsey-5-15 ramsey upper lean angeltveit-mckay-2019-2024 1341 1341.0 ramsey-6-6 ramsey upper lean angeltveit-mckay-2019-2024 160 160.0 ramsey-6-7 ramsey lower witness exoo-tatarevic-2015 115 115.0 ramsey-6-7 ramsey upper lean angeltveit-mckay-2019-2024 270 270.0 ramsey-6-8 ramsey lower witness exoo-tatarevic-2015 134 134.0 ramsey-6-8 ramsey upper lean angeltveit-mckay-2019-2024 423 423.0 ramsey-6-9 ramsey lower witness kuznetsov-2016 183 183.0 ramsey-6-9 ramsey upper lean angeltveit-mckay-2019-2024 651 651.0 ramsey-6-10 ramsey lower witness kuznetsov-2016 204 204.0 ramsey-6-10 ramsey upper lean angeltveit-mckay-2019-2024 944 944.0 ramsey-6-11 ramsey lower witness tatarevic-2020 262 262.0 ramsey-6-11 ramsey upper lean angeltveit-mckay-2019-2024 1346 1346.0 ramsey-6-12 ramsey lower witness kuznetsov-2016 294 294.0 ramsey-6-12 ramsey upper lean angeltveit-mckay-2019-2024 1855 1855.0 ramsey-6-13 ramsey lower witness kuznetsov-2016 347 347.0 ramsey-6-13 ramsey upper lean angeltveit-mckay-2019-2024 2499 2499.0 ramsey-6-14 ramsey upper lean angeltveit-mckay-2019-2024 3301 3301.0 ramsey-6-15 ramsey lower witness trivial 401 401.0 ramsey-6-15 ramsey upper lean angeltveit-mckay-2019-2024 4305 4305.0 ramsey-7-7 ramsey upper lean angeltveit-mckay-2019-2024 492 492.0 ramsey-7-8 ramsey lower witness tatarevic-2020 219 219.0 ramsey-7-8 ramsey upper lean angeltveit-mckay-2019-2024 832 832.0 ramsey-7-9 ramsey lower witness kuznetsov-2016 252 252.0 ramsey-7-9 ramsey upper lean angeltveit-mckay-2019-2024 1368 1368.0 ramsey-7-10 ramsey lower witness kuznetsov-2016 292 292.0 ramsey-7-10 ramsey upper lean angeltveit-mckay-2019-2024 2119 2119.0 ramsey-7-11 ramsey lower witness xu-xie-e-r-2004 405 405.0 ramsey-7-11 ramsey upper lean angeltveit-mckay-2019-2024 3197 3197.0 ramsey-7-12 ramsey lower witness xiaodong-s-r-2011 417 417.0 ramsey-7-12 ramsey upper lean angeltveit-mckay-2019-2024 4665 4665.0 ramsey-7-13 ramsey lower witness xu-xie-radziszowski-2004 511 511.0 ramsey-7-13 ramsey upper lean angeltveit-mckay-2019-2024 6653 6653.0 ramsey-7-14 ramsey upper lean angeltveit-mckay-2019-2024 9260 9260.0 ramsey-7-15 ramsey upper lean angeltveit-mckay-2019-2024 12635 12635.0 12,635 ramsey-8-8 ramsey upper lean angeltveit-mckay-2019-2024 1518 1518.0 ramsey-8-9 ramsey lower witness kuznetsov-2016 329 329.0 ramsey-8-9 ramsey upper lean angeltveit-mckay-2019-2024 2662 2662.0 ramsey-8-10 ramsey lower witness kuznetsov-2016 343 343.0 ramsey-8-10 ramsey upper lean angeltveit-mckay-2019-2024 4402 4402.0 ramsey-8-11 ramsey lower witness trivial 457 457.0 ramsey-8-11 ramsey upper lean angeltveit-mckay-2019-2024 7040 7040.0 ramsey-8-12 ramsey upper lean angeltveit-mckay-2019-2024 10836 10836.0 10,836 ramsey-8-13 ramsey lower witness xu-xie-e-r-2004 817 817.0 ramsey-8-13 ramsey upper lean huang-w-s-y-z-h-2007 27485 27485.0 27,485 ramsey-8-14 ramsey upper lean huang-w-s-y-z-h-2007 41525 41525.0 41,525 ramsey-8-15 ramsey lower witness trivial 873 873.0 ramsey-8-15 ramsey upper lean huang-w-s-y-z-h-2007 63609 63609.0 63,609 ramsey-9-9 ramsey lower witness mathon-1987 565 565.0 ramsey-9-9 ramsey upper lean angeltveit-mckay-2019-2024 4956 4956.0 ramsey-9-10 ramsey lower witness xiaodong-s-r-2011 581 581.0 ramsey-9-10 ramsey upper lean angeltveit-mckay-2019-2024 8675 8675.0 ramsey-9-11 ramsey upper lean angeltveit-mckay-2019-2024 14631 14631.0 14,631 ramsey-9-12 ramsey upper lean huang-w-s-y-z-h-2007 38832 38832.0 38,832 ramsey-9-13 ramsey upper lean huang-w-s-y-z-h-2007 64864 64864.0 64,864 ramsey-10-10 ramsey lower witness mathon-1987 798 798.0 ramsey-10-10 ramsey upper lean angeltveit-mckay-2019-2024 16064 16064.0 16,064 ramsey-10-11 ramsey upper lean huang-w-s-y-z-h-2007 45881 45881.0 45,881 ramsey-10-12 ramsey upper lean huang-w-s-y-z-h-2007 81123 81123.0 81,123 ramsey-10-15 ramsey lower witness trivial 1313 1313.0 square-packing-in-square-2 square-packing lower square-packing-in-square-2-lower-sqrt2 lean ejc-ds7-packing-unit-squares 2 2.0 \sqrt{2} 1.414214 ≈1.414214 square-packing-in-square-3 square-packing lower square-packing-in-square-3-lower-sqrt3 lean ejc-ds7-packing-unit-squares 2 2.0 \sqrt{3} 1.732051 ≈1.732051 square-packing-in-square-5 square-packing lower square-packing-in-square-5-lower-sqrt5 lean gobel-1979 2 + \frac{1}{\sqrt{2}} 2.707107 ≈2.707107 \sqrt{5} 2.236068 ≈2.236068 square-packing-in-square-5 square-packing upper square-packing-in-square-5-upper-3 lean gobel-1979 2 + \frac{1}{\sqrt{2}} 2.707107 ≈2.707107 3 3.0 square-packing-in-square-6 square-packing lower square-packing-in-square-6-lower-sqrt6 lean kearney-shiu-2002 3 3.0 \sqrt{6} 2.44949 ≈2.44949 square-packing-in-square-7 square-packing lower square-packing-in-square-7-lower-sqrt7 lean ejc-ds7-packing-unit-squares 3 3.0 \sqrt{7} 2.645751 ≈2.645751 square-packing-in-square-8 square-packing lower square-packing-in-square-8-lower-sqrt8 lean ejc-ds7-packing-unit-squares 3 3.0 \sqrt{8} 2.828427 ≈2.828427 square-packing-in-square-10 square-packing lower square-packing-in-square-10-lower-sqrt10 lean stromquist-2003 3 + \frac{1}{\sqrt{2}} 3.707107 ≈3.707107 \sqrt{10} 3.162278 ≈3.162278 square-packing-in-square-10 square-packing upper square-packing-in-square-10-upper-4 lean gobel-1979 3 + \frac{1}{\sqrt{2}} 3.707107 ≈3.707107 4 4.0 square-packing-in-square-11 square-packing lower square-packing-in-square-11-lower-sqrt11 lean ejc-ds7-packing-unit-squares 2 + \frac{4}{\sqrt{5}} 3.788854 ≈3.788854 \sqrt{11} 3.316625 ≈3.316625 square-packing-in-square-11 square-packing upper square-packing-in-square-11-upper-4 lean ejc-ds7-packing-unit-squares {\approx}3.8771 3.8771 4 4.0 square-packing-in-square-12 square-packing lower square-packing-in-square-12-lower-sqrt12 lean ejc-ds7-packing-unit-squares 2 + \frac{4}{\sqrt{5}} 3.788854 ≈3.788854 \sqrt{12} 3.464102 ≈3.464102 square-packing-in-square-13 square-packing lower square-packing-in-square-13-lower-sqrt13 lean bentz-2010 4 4.0 \sqrt{13} 3.605551 ≈3.605551 square-packing-in-square-14 square-packing lower square-packing-in-square-14-lower-sqrt14 lean ejc-ds7-packing-unit-squares 4 4.0 \sqrt{14} 3.741657 ≈3.741657 square-packing-in-square-15 square-packing lower square-packing-in-square-15-lower-sqrt15 lean ejc-ds7-packing-unit-squares 4 4.0 \sqrt{15} 3.872983 ≈3.872983 square-packing-in-square-17 square-packing lower square-packing-in-square-17-lower-sqrt17 lean ejc-ds7-packing-unit-squares \frac{40\sqrt{2}+19}{17} 4.445208 ≈4.445208 \sqrt{17} 4.123106 ≈4.123106 square-packing-in-square-17 square-packing upper square-packing-in-square-17-upper-5 lean ejc-ds7-packing-unit-squares {\approx}4.6755 4.6755 5 5.0 square-packing-in-square-18 square-packing lower square-packing-in-square-18-lower-sqrt18 lean ejc-ds7-packing-unit-squares \frac{40\sqrt{2}+19}{17} 4.445208 ≈4.445208 \sqrt{18} 4.242641 ≈4.242641 square-packing-in-square-18 square-packing upper square-packing-in-square-18-upper-5 lean ejc-ds7-packing-unit-squares \frac{7+\sqrt{7}}{2} 4.822876 ≈4.822876 5 5.0 square-packing-in-square-19 square-packing lower square-packing-in-square-19-lower-sqrt19 lean ejc-ds7-packing-unit-squares 6\sqrt{2}-4 4.485281 ≈4.485281 \sqrt{19} 4.358899 ≈4.358899 square-packing-in-square-19 square-packing upper square-packing-in-square-19-upper-5 lean ejc-ds7-packing-unit-squares 3+\frac{4\sqrt{2}}{3} 4.885618 ≈4.885618 5 5.0 square-packing-in-square-20 square-packing lower square-packing-in-square-20-lower-sqrt20 lean ejc-ds7-packing-unit-squares 6\sqrt{2}-4 4.485281 ≈4.485281 \sqrt{20} 4.472136 ≈4.472136 square-packing-in-square-21 square-packing lower square-packing-in-square-21-lower-sqrt21 lean ejc-ds7-packing-unit-squares 4.7438 4.7438 \sqrt{21} 4.582576 ≈4.582576 square-packing-in-square-22 square-packing lower square-packing-in-square-22-lower-sqrt22 lean bentz-2016 5 5.0 \sqrt{22} 4.690416 ≈4.690416 square-packing-in-square-23 square-packing lower square-packing-in-square-23-lower-sqrt23 lean nagamochi-2005 5 5.0 \sqrt{23} 4.795832 ≈4.795832 square-packing-in-square-24 square-packing lower square-packing-in-square-24-lower-sqrt24 lean ejc-ds7-packing-unit-squares 5 5.0 \sqrt{24} 4.898979 ≈4.898979 square-packing-in-square-26 square-packing lower square-packing-in-square-26-lower-sqrt26 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{27+2\sqrt{10}}{13} 5.391854 ≈5.391854 \sqrt{26} 5.09902 ≈5.09902 square-packing-in-square-26 square-packing upper square-packing-in-square-26-upper-6 lean ejc-ds7-packing-unit-squares \frac{7}{2}+\frac{3\sqrt{2}}{2} 5.62132 ≈5.62132 6 6.0 square-packing-in-square-27 square-packing lower square-packing-in-square-27-lower-sqrt27 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{27+2\sqrt{10}}{13} 5.391854 ≈5.391854 \sqrt{27} 5.196152 ≈5.196152 square-packing-in-square-27 square-packing upper square-packing-in-square-27-upper-6 lean gobel-1979 5+\frac{1}{\sqrt{2}} 5.707107 ≈5.707107 6 6.0 square-packing-in-square-28 square-packing lower square-packing-in-square-28-lower-sqrt28 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{6}{\sqrt{5}} 5.511709 ≈5.511709 \sqrt{28} 5.291503 ≈5.291503 square-packing-in-square-28 square-packing upper square-packing-in-square-28-upper-6 lean ellsworth-2025-12 {\approx}5.8244 5.8244 6 6.0 square-packing-in-square-29 square-packing lower square-packing-in-square-29-lower-sqrt29 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{6}{\sqrt{5}} 5.511709 ≈5.511709 \sqrt{29} 5.385165 ≈5.385165 square-packing-in-square-29 square-packing upper square-packing-in-square-29-upper-6 lean schadt-2025-12 {\approx}5.9338 5.9338 6 6.0 square-packing-in-square-30 square-packing lower square-packing-in-square-30-lower-sqrt30 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{6}{\sqrt{5}} 5.511709 ≈5.511709 \sqrt{30} 5.477226 ≈5.477226 square-packing-in-square-31 square-packing lower square-packing-in-square-31-lower-sqrt31 lean ejc-ds7-packing-unit-squares 5.6415 5.6415 \sqrt{31} 5.567764 ≈5.567764 square-packing-in-square-33 square-packing lower square-packing-in-square-33-lower-sqrt33 lean bentz-2016 6 6.0 \sqrt{33} 5.744563 ≈5.744563 square-packing-in-square-34 square-packing lower square-packing-in-square-34-lower-sqrt34 lean nagamochi-2005 6 6.0 \sqrt{34} 5.830952 ≈5.830952 square-packing-in-square-35 square-packing lower square-packing-in-square-35-lower-sqrt35 lean ejc-ds7-packing-unit-squares 6 6.0 \sqrt{35} 5.91608 ≈5.91608 square-packing-in-square-37 square-packing lower square-packing-in-square-37-lower-sqrt37 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{113+10\sqrt{3}}{37} 6.350603 ≈6.350603 \sqrt{37} 6.082763 ≈6.082763 square-packing-in-square-37 square-packing upper square-packing-in-square-37-upper-7 lean ejc-ds7-packing-unit-squares {\approx}6.5986 6.5986 7 7.0 square-packing-in-square-38 square-packing lower square-packing-in-square-38-lower-sqrt38 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{113+10\sqrt{3}}{37} 6.350603 ≈6.350603 \sqrt{38} 6.164414 ≈6.164414 square-packing-in-square-38 square-packing upper square-packing-in-square-38-upper-7 lean gobel-1979 6+\frac{1}{\sqrt{2}} 6.707107 ≈6.707107 7 7.0 square-packing-in-square-39 square-packing lower square-packing-in-square-39-lower-sqrt39 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{113+10\sqrt{3}}{37} 6.350603 ≈6.350603 \sqrt{39} 6.244998 ≈6.244998 square-packing-in-square-39 square-packing upper square-packing-in-square-39-upper-7 lean schadt-2026-01 {\approx}6.8107 6.8107 7 7.0 square-packing-in-square-40 square-packing lower square-packing-in-square-40-lower-sqrt40 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{8}{\sqrt{5}} 6.406136 ≈6.406136 \sqrt{40} 6.324555 ≈6.324555 square-packing-in-square-40 square-packing upper square-packing-in-square-40-upper-7 lean ejc-ds7-packing-unit-squares 4+2\sqrt{2} 6.828427 ≈6.828427 7 7.0 square-packing-in-square-41 square-packing lower square-packing-in-square-41-lower-sqrt41 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{8}{\sqrt{5}} 6.406136 ≈6.406136 \sqrt{41} 6.403124 ≈6.403124 square-packing-in-square-41 square-packing upper square-packing-in-square-41-upper-7 lean schadt-2025-12 {\approx}6.9267 6.9267 7 7.0 square-packing-in-square-46 square-packing lower square-packing-in-square-46-lower-sqrt46 lean bentz-2010 7 7.0 \sqrt{46} 6.78233 ≈6.78233 square-packing-in-square-47 square-packing lower square-packing-in-square-47-lower-sqrt47 lean nagamochi-2005 7 7.0 \sqrt{47} 6.855655 ≈6.855655 square-packing-in-square-48 square-packing lower square-packing-in-square-48-lower-sqrt48 lean nagamochi-2005 7 7.0 \sqrt{48} 6.928203 ≈6.928203 square-packing-in-square-50 square-packing lower square-packing-in-square-50-lower-sqrt50 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 \sqrt{50} 7.071068 ≈7.071068 square-packing-in-square-50 square-packing upper square-packing-in-square-50-upper-8 lean schadt-2025-12 7+\frac{4}{7} 7.571429 ≈7.571429 8 8.0 square-packing-in-square-51 square-packing lower square-packing-in-square-51-lower-sqrt51 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 \sqrt{51} 7.141428 ≈7.141428 square-packing-in-square-51 square-packing upper square-packing-in-square-51-upper-8 lean schadt-2026-01 {\approx}7.7008 7.7008 8 8.0 square-packing-in-square-52 square-packing lower square-packing-in-square-52-lower-sqrt52 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 \sqrt{52} 7.211103 ≈7.211103 square-packing-in-square-52 square-packing upper square-packing-in-square-52-upper-8 lean gobel-1979 7+\frac{1}{\sqrt{2}} 7.707107 ≈7.707107 8 8.0 square-packing-in-square-53 square-packing lower square-packing-in-square-53-lower-sqrt53 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{101+3\sqrt{14}}{25} 7.317426 ≈7.317426 \sqrt{53} 7.28011 ≈7.28011 square-packing-in-square-53 square-packing upper square-packing-in-square-53-upper-8 lean ellsworth-2026-02 \frac{13}{2}+\frac{\sqrt{7}}{2} 7.822876 ≈7.822876 8 8.0 square-packing-in-square-54 square-packing upper square-packing-in-square-54-upper-8 lean devincentis-2014 7-\frac{\sqrt{2}}{2}+\sqrt{1+\sqrt{2}} 7.846667 ≈7.846667 8 8.0 square-packing-in-square-55 square-packing upper square-packing-in-square-55-upper-8 lean ellsworth-2026-02 {\approx}7.9458 7.9458 8 8.0 square-packing-in-square-62 square-packing lower square-packing-in-square-62-lower-sqrt62 lean nagamochi-2005 8 8.0 \sqrt{62} 7.874008 ≈7.874008 square-packing-in-square-63 square-packing lower square-packing-in-square-63-lower-sqrt63 lean nagamochi-2005 8 8.0 \sqrt{63} 7.937254 ≈7.937254 square-packing-in-square-65 square-packing lower square-packing-in-square-65-lower-sqrt65 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 \sqrt{65} 8.062258 ≈8.062258 square-packing-in-square-65 square-packing upper square-packing-in-square-65-upper-9 lean ejc-ds7-packing-unit-squares 5+\frac{5}{\sqrt{2}} 8.535534 ≈8.535534 9 9.0 square-packing-in-square-66 square-packing lower square-packing-in-square-66-lower-sqrt66 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 \sqrt{66} 8.124038 ≈8.124038 square-packing-in-square-66 square-packing upper square-packing-in-square-66-upper-9 lean ejc-ds7-packing-unit-squares 3+4\sqrt{2} 8.656854 ≈8.656854 9 9.0 square-packing-in-square-67 square-packing lower square-packing-in-square-67-lower-sqrt67 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 \sqrt{67} 8.185353 ≈8.185353 square-packing-in-square-67 square-packing upper square-packing-in-square-67-upper-9 lean gobel-1979 8+\frac{1}{\sqrt{2}} 8.707107 ≈8.707107 9 9.0 square-packing-in-square-68 square-packing lower square-packing-in-square-68-lower-sqrt68 lean ejc-ds7-packing-unit-squares 2\sqrt{2}+\frac{71}{13} 8.289966 ≈8.289966 \sqrt{68} 8.246211 ≈8.246211 square-packing-in-square-68 square-packing upper square-packing-in-square-68-upper-9 lean loyd-2026 {\approx}8.7988 8.7988 9 9.0 square-packing-in-square-69 square-packing upper square-packing-in-square-69-upper-9 lean hmbelvedere-2026 {\approx}8.8272 8.8272 9 9.0 square-packing-in-square-70 square-packing upper square-packing-in-square-70-upper-9 lean devincentis-2014 {\approx}8.8817 8.8817 9 9.0 square-packing-in-square-71 square-packing upper square-packing-in-square-71-upper-9 lean schadt-2025-12 {\approx}8.9441 8.9441 9 9.0 square-packing-in-square-79 square-packing lower square-packing-in-square-79-lower-sqrt79 lean nagamochi-2005 9 9.0 \sqrt{79} 8.888194 ≈8.888194 square-packing-in-square-80 square-packing lower square-packing-in-square-80-lower-sqrt80 lean nagamochi-2005 9 9.0 \sqrt{80} 8.944272 ≈8.944272 square-packing-in-square-82 square-packing lower square-packing-in-square-82-lower-sqrt82 lean ejc-ds7-packing-unit-squares {\approx}9.2667 9.2667 \sqrt{82} 9.055385 ≈9.055385 square-packing-in-square-82 square-packing upper square-packing-in-square-82-upper-10 lean ejc-ds7-packing-unit-squares 6+\frac{5}{\sqrt{2}} 9.535534 ≈9.535534 10 10.0 square-packing-in-square-83 square-packing lower square-packing-in-square-83-lower-sqrt83 lean ejc-ds7-packing-unit-squares {\approx}9.2667 9.2667 \sqrt{83} 9.110434 ≈9.110434 square-packing-in-square-83 square-packing upper square-packing-in-square-83-upper-10 lean chang-2026 {\approx}9.6348 9.6348 10 10.0 square-packing-in-square-84 square-packing lower square-packing-in-square-84-lower-sqrt84 lean ejc-ds7-packing-unit-squares {\approx}9.2667 9.2667 \sqrt{84} 9.165151 ≈9.165151 square-packing-in-square-84 square-packing upper square-packing-in-square-84-upper-10 lean gobel-1979 9+\frac{1}{\sqrt{2}} 9.707107 ≈9.707107 10 10.0 square-packing-in-square-85 square-packing lower square-packing-in-square-85-lower-sqrt85 lean ejc-ds7-packing-unit-squares {\approx}9.2667 9.2667 \sqrt{85} 9.219544 ≈9.219544 square-packing-in-square-85 square-packing upper square-packing-in-square-85-upper-10 lean ejc-ds7-packing-unit-squares \frac{11}{2}+3\sqrt{2} 9.742641 ≈9.742641 10 10.0 square-packing-in-square-86 square-packing upper square-packing-in-square-86-upper-10 lean ejc-ds7-packing-unit-squares \frac{17+\sqrt{7}}{2} 9.822876 ≈9.822876 10 10.0 square-packing-in-square-87 square-packing upper square-packing-in-square-87-upper-10 lean chang-2026 {\approx}9.8388 9.8388 10 10.0 square-packing-in-square-88 square-packing upper square-packing-in-square-88-upper-10 lean cantrell-ellsworth-2025 {\approx}9.8882 9.8882 10 10.0 square-packing-in-square-89 square-packing upper square-packing-in-square-89-upper-10 lean ejc-ds7-packing-unit-squares 5+\frac{7}{\sqrt{2}} 9.949747 ≈9.949747 10 10.0 square-packing-in-square-98 square-packing lower square-packing-in-square-98-lower-sqrt98 lean nagamochi-2005 10 10.0 \sqrt{98} 9.899495 ≈9.899495 square-packing-in-square-99 square-packing lower square-packing-in-square-99-lower-sqrt99 lean nagamochi-2005 10 10.0 \sqrt{99} 9.949874 ≈9.949874 kissing-number-1 kissing-number upper lean trivial 2 2.0 kissing-number-2 kissing-number upper lean trivial 6 6.0 kissing-number-3 kissing-number upper lean schutte-van-der-waerden-1953 12 12.0 kissing-number-4 kissing-number upper lean musin-2003 24 24.0 kissing-number-5 kissing-number upper lean mittelmann-vallentin-2009 44 44.0 kissing-number-6 kissing-number upper lean de-laat-leijenhorst-de-muinck-keizer-2024 77 77.0 kissing-number-7 kissing-number upper lean mittelmann-vallentin-2009 134 134.0 kissing-number-8 kissing-number upper lean odlyzko-sloane-1979 240 240.0 kissing-number-9 kissing-number lower kissing-number-9-lower-272 witness leech-sloane-1971 306 306.0 272 272.0 kissing-number-9 kissing-number upper lean machado-oliveira-2018 363 363.0 kissing-number-10 kissing-number lower kissing-number-10-lower-336 witness ganzhinov-2022 510 510.0 336 336.0 kissing-number-10 kissing-number upper lean machado-oliveira-2018 553 553.0 kissing-number-11 kissing-number lower kissing-number-11-lower-438 witness bianchi-et-al-2026 604 604.0 438 438.0 kissing-number-11 kissing-number upper lean leijenhorst-de-laat-2022 868 868.0 kissing-number-12 kissing-number lower kissing-number-12-lower-756 witness takhanov-assylbekov-yun-2026 841 841.0 756 756.0 kissing-number-12 kissing-number upper lean leijenhorst-de-laat-2022 1355 1355.0 kissing-number-13 kissing-number lower kissing-number-13-lower-906 witness zinoviev-ericson-1999 1154 1154.0 906 906.0 kissing-number-13 kissing-number upper lean leijenhorst-de-laat-2022 2064 2064.0 kissing-number-14 kissing-number lower kissing-number-14-lower-1422 witness ganzhinov-2022 1932 1932.0 1422 1422.0 kissing-number-14 kissing-number upper lean leijenhorst-de-laat-2022 3174 3174.0 kissing-number-15 kissing-number lower kissing-number-15-lower-2340 witness leech-sloane-1971 2564 2564.0 2340 2340.0 kissing-number-15 kissing-number upper lean leijenhorst-de-laat-2022 4853 4853.0 kissing-number-16 kissing-number upper lean leijenhorst-de-laat-2022 7320 7320.0 kissing-number-17 kissing-number lower kissing-number-17-lower-5346 witness cohn-li-2024 5730 5730.0 5346 5346.0 kissing-number-17 kissing-number upper lean leijenhorst-de-laat-2022 10978 10978.0 10,978 kissing-number-18 kissing-number lower kissing-number-18-lower-7398 witness kravatskiy-2026 8358 8358.0 7398 7398.0 kissing-number-18 kissing-number upper lean leijenhorst-de-laat-2022 16406 16406.0 16,406 kissing-number-19 kissing-number lower kissing-number-19-lower-10668 witness li-2026 12460 12460.0 12,460 10668 10668.0 10,668 kissing-number-19 kissing-number upper lean leijenhorst-de-laat-2022 24417 24417.0 24,417 kissing-number-20 kissing-number lower kissing-number-20-lower-17400 witness cohn-li-2024 19448 19448.0 19,448 17400 17400.0 17,400 kissing-number-20 kissing-number upper lean leijenhorst-de-laat-2022 36195 36195.0 36,195 kissing-number-21 kissing-number lower kissing-number-21-lower-27720 witness li-2026 31560 31560.0 31,560 27720 27720.0 27,720 kissing-number-21 kissing-number upper lean leijenhorst-de-laat-2022 53524 53524.0 53,524 kissing-number-22 kissing-number upper lean leijenhorst-de-laat-2022 80810 80810.0 80,810 kissing-number-23 kissing-number upper lean leijenhorst-de-laat-2022 122351 122351.0 122,351 kissing-number-24 kissing-number upper lean odlyzko-sloane-1979 196560 196560.0 196,560 degree-diameter-3-2 degree-diameter upper lean wikipedia-degree-diameter 10 10.0 degree-diameter-3-3 degree-diameter upper lean elspasgraphs 20 20.0 degree-diameter-3-4 degree-diameter upper lean buset-2000 38 38.0 degree-diameter-3-5 degree-diameter lower degree-diameter-3-5-lower-64 witness afygraph 70 70.0 64 64.0 degree-diameter-3-6 degree-diameter lower degree-diameter-3-6-lower-64 witness exoo-1998-05 132 132.0 64 64.0 degree-diameter-3-7 degree-diameter lower degree-diameter-3-7-lower-162 witness bhakar-2026-10 200 200.0 162 162.0 degree-diameter-3-8 degree-diameter lower degree-diameter-3-8-lower-272 witness jianxiang-chen-2018 360 360.0 272 272.0 degree-diameter-3-9 degree-diameter lower degree-diameter-3-9-lower-506 witness exoo-2008-01 600 600.0 506 506.0 degree-diameter-3-10 degree-diameter lower degree-diameter-3-10-lower-820 witness conder-2006 1250 1250.0 820 820.0 degree-diameter-4-2 degree-diameter upper lean elspasgraphs 15 15.0 degree-diameter-4-4 degree-diameter lower degree-diameter-4-4-lower-84 witness bhakar-2026-08 104 104.0 84 84.0 degree-diameter-4-5 degree-diameter lower degree-diameter-4-5-lower-205 witness delorme85agraphs 364 364.0 205 205.0 degree-diameter-4-6 degree-diameter lower degree-diameter-4-6-lower-513 witness bhakar-2026-10 760 760.0 513 513.0 degree-diameter-4-7 degree-diameter lower degree-diameter-4-7-lower-1155 witness yugeswardeenoo-2026-10 1344 1344.0 1155 1155.0 degree-diameter-4-8 degree-diameter lower witness loz-siran-2008 3243 3243.0 degree-diameter-4-9 degree-diameter lower witness bhakar-2026-10 7884 7884.0 degree-diameter-4-10 degree-diameter lower witness bhakar-2026-10 19306 19306.0 19,306 degree-diameter-5-2 degree-diameter upper lean elspasgraphs 24 24.0 degree-diameter-5-3 degree-diameter lower degree-diameter-5-3-lower-54 witness exoo-2001 72 72.0 54 54.0 degree-diameter-5-4 degree-diameter lower degree-diameter-5-4-lower-210 witness rajiv-2026-09b 252 252.0 210 210.0 degree-diameter-5-5 degree-diameter lower degree-diameter-5-5-lower-506 witness gupta-2026-09 650 650.0 506 506.0 degree-diameter-5-6 degree-diameter lower witness bhakar-2026-10 2836 2836.0 degree-diameter-5-7 degree-diameter lower witness bhakar-2026-10 6000 6000.0 degree-diameter-5-8 degree-diameter lower witness bhakar-2026-10 18810 18810.0 18,810 degree-diameter-5-9 degree-diameter lower witness bhakar-2026-10 60686 60686.0 60,686 degree-diameter-5-10 degree-diameter lower witness bhakar-2026-10 202550 202550.0 202,550 degree-diameter-6-2 degree-diameter upper lean molodtsov-2006 32 32.0 degree-diameter-6-3 degree-diameter lower degree-diameter-6-3-lower-90 witness de-messieres-2026-10 120 120.0 90 90.0 degree-diameter-6-4 degree-diameter lower degree-diameter-6-4-lower-355 witness rajiv-2026-09b 441 441.0 355 355.0 degree-diameter-6-5 degree-diameter lower degree-diameter-6-5-lower-1395 witness rajiv-2026-08 1518 1518.0 1395 1395.0 degree-diameter-6-6 degree-diameter lower witness yugeswardeenoo-2026-10 8802 8802.0 degree-diameter-6-7 degree-diameter lower witness gupta-2026-09 20400 20400.0 20,400 degree-diameter-6-8 degree-diameter lower witness bhakar-2026-10 80050 80050.0 80,050 degree-diameter-6-9 degree-diameter lower witness canale12graphs 331387 331387.0 331,387 degree-diameter-6-10 degree-diameter lower witness bhakar-2026-10 1394189 1394189.0 1,394,189 degree-diameter-7-2 degree-diameter upper lean wikipedia-degree-diameter 50 50.0 degree-diameter-7-3 degree-diameter lower degree-diameter-7-3-lower-140 witness rajiv-2026-09d 170 170.0 140 140.0 degree-diameter-7-4 degree-diameter lower degree-diameter-7-4-lower-602 witness de-messieres-2026-10 684 684.0 602 602.0 degree-diameter-7-5 degree-diameter lower witness yugeswardeenoo-2026-10 2810 2810.0 degree-diameter-7-6 degree-diameter lower witness bhakar-2026-10 12654 12654.0 12,654 degree-diameter-7-7 degree-diameter lower witness rajiv-2026-09b 56952 56952.0 56,952 degree-diameter-7-8 degree-diameter lower witness bhakar-2026-10 264440 264440.0 264,440 degree-diameter-7-9 degree-diameter lower witness bhakar-2026-10 1332774 1332774.0 1,332,774 degree-diameter-7-10 degree-diameter lower witness yugeswardeenoo-2026-10 6645690 6645690.0 6,645,690 degree-diameter-8-4 degree-diameter lower degree-diameter-8-4-lower-1029 witness loz-siran-2008 1100 1100.0 1029 1029.0 degree-diameter-8-5 degree-diameter lower witness rajiv-2026-09b 5334 5334.0 degree-diameter-8-6 degree-diameter lower witness yugeswardeenoo-2026-10 40560 40560.0 40,560 degree-diameter-8-7 degree-diameter lower witness bhakar-2026-10 139679 139679.0 139,679 degree-diameter-8-8 degree-diameter lower witness bhakar-2026-10 802890 802890.0 802,890 degree-diameter-8-9 degree-diameter lower witness bhakar-2026-10 4601361 4601361.0 4,601,361 degree-diameter-8-10 degree-diameter lower witness rajiv-2026-10 26988069 26988069.0 26,988,069 degree-diameter-9-3 degree-diameter lower degree-diameter-9-3-lower-256 witness delorme85agraphs 585 585.0 256 256.0 degree-diameter-9-4 degree-diameter lower degree-diameter-9-4-lower-1254 witness comellas-2026-10 1768 1768.0 1254 1254.0 degree-diameter-9-5 degree-diameter lower witness bhakar-2026-10 9020 9020.0 degree-diameter-9-6 degree-diameter lower witness yugeswardeenoo-2026-10 77418 77418.0 77,418 degree-diameter-9-7 degree-diameter lower witness bhakar-2026-10 309510 309510.0 309,510 degree-diameter-9-8 degree-diameter lower witness yugeswardeenoo-2026-10 1961496 1961496.0 1,961,496 degree-diameter-9-9 degree-diameter lower witness bhakar-2026-10 13219318 13219318.0 13,219,318 degree-diameter-9-10 degree-diameter lower witness yugeswardeenoo-2026-10 89658816 89658816.0 89,658,816 degree-diameter-10-3 degree-diameter lower degree-diameter-10-3-lower-366 witness delorme85agraphs 650 650.0 366 366.0 degree-diameter-10-4 degree-diameter lower witness rajiv-2026-10 2556 2556.0 degree-diameter-10-5 degree-diameter lower witness rajiv-2026-09a 33397 33397.0 33,397 degree-diameter-10-6 degree-diameter lower witness yugeswardeenoo-2026-10 137180 137180.0 137,180 degree-diameter-10-7 degree-diameter lower witness bhakar-2026-10 624690 624690.0 624,690 degree-diameter-10-8 degree-diameter lower witness yugeswardeenoo-2026-10 4524979 4524979.0 4,524,979 degree-diameter-10-9 degree-diameter lower witness bhakar-2026-10 34913494 34913494.0 34,913,494 degree-diameter-10-10 degree-diameter lower witness yugeswardeenoo-2026-10 265782337 265782337.0 265,782,337 degree-diameter-11-2 degree-diameter lower degree-diameter-11-2-lower-98 witness yugeswardeenoo-2026-09 106 106.0 98 98.0 degree-diameter-11-3 degree-diameter lower degree-diameter-11-3-lower-420 witness delorme85agraphs 715 715.0 420 420.0 degree-diameter-11-4 degree-diameter lower witness bhakar-2026-10 3645 3645.0 degree-diameter-11-5 degree-diameter lower witness yugeswardeenoo-2026-10 37628 37628.0 37,628 degree-diameter-11-6 degree-diameter lower witness yugeswardeenoo-2026-10 186033 186033.0 186,033 degree-diameter-11-7 degree-diameter lower witness bhakar-2026-10 1197748 1197748.0 1,197,748 degree-diameter-11-8 degree-diameter lower witness bhakar-2026-10 9739368 9739368.0 9,739,368 degree-diameter-11-9 degree-diameter lower witness bhakar-2026-10 81961120 81961120.0 81,961,120 degree-diameter-11-10 degree-diameter lower witness yugeswardeenoo-2026-10 697429356 697429356.0 697,429,356 degree-diameter-12-3 degree-diameter lower degree-diameter-12-3-lower-558 witness yugeswardeenoo-2026-10 810 810.0 558 558.0 degree-diameter-12-4 degree-diameter lower witness bhakar-2026-10 6156 6156.0 degree-diameter-12-5 degree-diameter lower witness yugeswardeenoo-2026-10 42342 42342.0 42,342 degree-diameter-12-6 degree-diameter lower witness yugeswardeenoo-2026-10 364032 364032.0 364,032 degree-diameter-12-7 degree-diameter lower witness yugeswardeenoo-2026-10 2115075 2115075.0 2,115,075 degree-diameter-12-8 degree-diameter lower witness yugeswardeenoo-2026-10 19218539 19218539.0 19,218,539 degree-diameter-12-9 degree-diameter lower witness bhakar-2026-10 179227730 179227730.0 179,227,730 degree-diameter-12-10 degree-diameter lower witness yugeswardeenoo-2026-10 1693183778 1693183778.0 1,693,183,778 degree-diameter-13-3 degree-diameter lower degree-diameter-13-3-lower-630 witness yugeswardeenoo-2026-10 972 972.0 630 630.0 degree-diameter-13-4 degree-diameter lower witness bhakar-2026-10 6804 6804.0 degree-diameter-13-5 degree-diameter lower witness yugeswardeenoo-2026-10 51417 51417.0 51,417 degree-diameter-13-6 degree-diameter lower witness yugeswardeenoo-2026-10 538740 538740.0 538,740 degree-diameter-13-7 degree-diameter lower witness bhakar-2026-10 3691038 3691038.0 3,691,038 degree-diameter-13-8 degree-diameter lower witness bhakar-2026-10 36275160 36275160.0 36,275,160 degree-diameter-13-9 degree-diameter lower witness yugeswardeenoo-2026-10 362847996 362847996.0 362,847,996 degree-diameter-13-10 degree-diameter lower witness yugeswardeenoo-2026-10 3789512750 3789512750.0 3,789,512,750 degree-diameter-14-3 degree-diameter lower degree-diameter-14-3-lower-791 witness rajiv-2026-10 1201 1201.0 791 791.0 degree-diameter-14-4 degree-diameter lower witness bhakar-2026-10 9720 9720.0 degree-diameter-14-5 degree-diameter lower witness badaoui-vaughan-2026-10 94186 94186.0 94,186 degree-diameter-14-6 degree-diameter lower witness yugeswardeenoo-2026-10 824124 824124.0 824,124 degree-diameter-14-7 degree-diameter lower witness gfsgraphs 6200460 6200460.0 6,200,460 degree-diameter-14-8 degree-diameter lower witness rajiv-2026-10 65017283 65017283.0 65,017,283 degree-diameter-14-9 degree-diameter lower witness yugeswardeenoo-2026-10 709728527 709728527.0 709,728,527 degree-diameter-14-10 degree-diameter lower witness bhakar-2026-10 8052187457 8052187457.0 8,052,187,457 degree-diameter-15-2 degree-diameter lower degree-diameter-15-2-lower-183 witness yugeswardeenoo-2026-09 190 190.0 183 183.0 degree-diameter-15-3 degree-diameter lower degree-diameter-15-3-lower-812 witness mccormick-2026-10 1620 1620.0 812 812.0 degree-diameter-15-4 degree-diameter lower witness yugeswardeenoo-2026-10 15552 15552.0 15,552 degree-diameter-15-5 degree-diameter lower witness yugeswardeenoo-2026-10 102060 102060.0 102,060 degree-diameter-15-6 degree-diameter lower witness yugeswardeenoo-2026-10 1428361 1428361.0 1,428,361 degree-diameter-15-7 degree-diameter lower witness bhakar-2026-10 9758988 9758988.0 9,758,988 degree-diameter-15-8 degree-diameter lower witness yugeswardeenoo-2026-10 110182818 110182818.0 110,182,818 degree-diameter-15-9 degree-diameter lower witness yugeswardeenoo-2026-10 1315254800 1315254800.0 1,315,254,800 degree-diameter-15-10 degree-diameter lower witness rajiv-2026-10 16021302724 16021302724.0 16,021,302,724 degree-diameter-16-2 degree-diameter lower degree-diameter-16-2-lower-183 witness rajiv-2026-09b 216 216.0 183 183.0 degree-diameter-16-3 degree-diameter lower degree-diameter-16-3-lower-1055 witness mizuno-2026-09 1920 1920.0 1055 1055.0 degree-diameter-16-4 degree-diameter lower witness amarel-et-al-2026 16384 16384.0 16,384 degree-diameter-16-5 degree-diameter lower witness rajiv-2026-10 153600 153600.0 153,600 degree-diameter-16-6 degree-diameter lower witness yugeswardeenoo-2026-10 1793786 1793786.0 1,793,786 degree-diameter-16-7 degree-diameter lower witness bhakar-2026-10 14995367 14995367.0 14,995,367 degree-diameter-16-8 degree-diameter lower witness yugeswardeenoo-2026-10 185488215 185488215.0 185,488,215 degree-diameter-16-9 degree-diameter lower witness yugeswardeenoo-2026-10 2345620783 2345620783.0 2,345,620,783 degree-diameter-16-10 degree-diameter lower witness bhakar-2026-10 29899503497 29899503497.0 29,899,503,497 degree-diameter-17-3 degree-diameter lower witness rajiv-2026-09d 2210 2210.0 degree-diameter-17-4 degree-diameter lower witness rajiv-2026-09c 19121 19121.0 19,121 degree-diameter-17-5 degree-diameter lower witness rajiv-2026-10 153600 153600.0 153,600 degree-diameter-17-6 degree-diameter lower witness loz-pineda-2010 3217872 3217872.0 3,217,872 degree-diameter-17-7 degree-diameter lower witness rajiv-2026-09d 20737440 20737440.0 20,737,440 degree-diameter-17-8 degree-diameter lower witness rajiv-2026-10 282355100 282355100.0 282,355,100 degree-diameter-17-9 degree-diameter lower witness rajiv-2026-10 3970800200 3970800200.0 3,970,800,200 degree-diameter-17-10 degree-diameter lower witness rajiv-2026-10 50125320600 50125320600.0 50,125,320,600 degree-diameter-18-3 degree-diameter lower witness rajiv-2026-09d 2210 2210.0 degree-diameter-18-4 degree-diameter lower witness rajiv-2026-09c 23956 23956.0 23,956 degree-diameter-18-5 degree-diameter lower witness rajiv-2026-09b 197316 197316.0 197,316 degree-diameter-18-6 degree-diameter lower witness loz-pineda-2010 4022340 4022340.0 4,022,340 degree-diameter-18-7 degree-diameter lower witness rajiv-2026-09d 29193120 29193120.0 29,193,120 degree-diameter-18-8 degree-diameter lower witness rajiv-2026-10 455904533 455904533.0 455,904,533 degree-diameter-18-9 degree-diameter lower witness rajiv-2026-10 6645271633 6645271633.0 6,645,271,633 degree-diameter-18-10 degree-diameter lower witness rajiv-2026-10 90017766839 90017766839.0 90,017,766,839 degree-diameter-19-3 degree-diameter lower witness rajiv-2026-09c 2783 2783.0 degree-diameter-19-4 degree-diameter lower witness rajiv-2026-09c 25050 25050.0 25,050 degree-diameter-19-5 degree-diameter lower witness rajiv-2026-09b 222972 222972.0 222,972 degree-diameter-19-6 degree-diameter lower witness loz-pineda-2010 4024707 4024707.0 4,024,707 degree-diameter-19-7 degree-diameter lower witness rajiv-2026-09d 41152320 41152320.0 41,152,320 degree-diameter-19-8 degree-diameter lower witness rajiv-2026-10 682205312 682205312.0 682,205,312 degree-diameter-19-9 degree-diameter lower witness rajiv-2026-10 10829019852 10829019852.0 10,829,019,852 degree-diameter-19-10 degree-diameter lower witness rajiv-2026-10 120461699776 120461699776.0 120,461,699,776 degree-diameter-20-3 degree-diameter lower witness rajiv-2026-10 2796 2796.0 degree-diameter-20-4 degree-diameter lower witness rajiv-2026-10 40000 40000.0 40,000 degree-diameter-20-5 degree-diameter lower witness rajiv-2026-08 450000 450000.0 450,000 degree-diameter-20-6 degree-diameter lower witness loz-pineda-2010 8947848 8947848.0 8,947,848 degree-diameter-20-7 degree-diameter lower witness loz-pineda-2010 55625185 55625185.0 55,625,185 degree-diameter-20-8 degree-diameter lower witness rajiv-2026-10 1051819147 1051819147.0 1,051,819,147 degree-diameter-20-9 degree-diameter lower witness rajiv-2026-10 16669570133 16669570133.0 16,669,570,133 degree-diameter-20-10 degree-diameter lower witness rajiv-2026-10 120461699776 120461699776.0 120,461,699,776 cage-3-7 cage lower cage-3-7-lower-22 lean ejc-ds16-cages 24 24.0 22 22.0 cage-3-9 cage lower cage-3-9-lower-46 lean ejc-ds16-cages 58 58.0 46 46.0 cage-3-9 cage upper witness ejc-ds16-cages 58 58.0 cage-3-10 cage lower cage-3-10-lower-62 lean ejc-ds16-cages 70 70.0 62 62.0 cage-3-10 cage upper witness ejc-ds16-cages 70 70.0 cage-3-11 cage lower cage-3-11-lower-94 lean ejc-ds16-cages 112 112.0 94 94.0 cage-3-11 cage upper witness ejc-ds16-cages 112 112.0 cage-3-12 cage upper witness ejc-ds16-cages 126 126.0 cage-3-13 cage lower cage-3-13-lower-190 lean ejc-ds16-cages 202 202.0 190 190.0 cage-3-13 cage upper witness ejc-ds16-cages 272 272.0 cage-3-14 cage lower cage-3-14-lower-254 lean ejc-ds16-cages 258 258.0 254 254.0 cage-3-14 cage upper witness ejc-ds16-cages 384 384.0 cage-3-15 cage lower cage-3-15-lower-382 lean ejc-ds16-cages 384 384.0 382 382.0 cage-3-15 cage upper witness ejc-ds16-cages 620 620.0 cage-3-16 cage lower cage-3-16-lower-510 lean ejc-ds16-cages 512 512.0 510 510.0 cage-3-16 cage upper witness exoo-et-al-2026 936 936.0 cage-4-5 cage lower cage-4-5-lower-17 lean ejc-ds16-cages 19 19.0 17 17.0 cage-4-5 cage upper witness ejc-ds16-cages 19 19.0 cage-4-7 cage lower cage-4-7-lower-53 lean wikipedia-cage 67 67.0 53 53.0 cage-4-7 cage upper witness ejc-ds16-cages 67 67.0 cage-4-9 cage upper witness exoo-et-al-2026 270 270.0 cage-4-10 cage upper witness exoo-et-al-2026 320 320.0 cage-4-12 cage upper witness ejc-ds16-cages 728 728.0 cage-5-5 cage lower cage-5-5-lower-26 lean ejc-ds16-cages 30 30.0 26 26.0 cage-5-5 cage upper witness ejc-ds16-cages 30 30.0 cage-5-7 cage upper witness ejc-ds16-cages 152 152.0 cage-5-10 cage upper witness exoo-circa-2012 1296 1296.0 cage-5-11 cage upper witness araujopardo-2010 2688 2688.0 cage-5-12 cage upper witness ejc-ds16-cages 2730 2730.0 cage-6-5 cage lower cage-6-5-lower-37 lean ejc-ds16-cages 40 40.0 37 37.0 cage-6-5 cage upper witness ejc-ds16-cages 40 40.0 cage-6-7 cage upper witness ejc-ds16-cages 294 294.0 cage-6-12 cage upper witness ejc-ds16-cages 7812 7812.0 cage-7-6 cage lower cage-7-6-lower-86 lean ejc-ds16-cages 90 90.0 86 86.0 cage-7-6 cage upper witness ejc-ds16-cages 90 90.0 cage-7-8 cage upper witness ejc-ds16-cages 672 672.0 cage-7-12 cage upper witness ejc-ds16-cages 32928 32928.0 32,928 cage-8-5 cage lower cage-8-5-lower-65 lean ejc-ds16-cages 67 67.0 65 65.0 cage-8-5 cage upper witness ejc-ds16-cages 80 80.0 cage-8-12 cage upper witness ejc-ds16-cages 39216 39216.0 39,216 cage-9-5 cage lower cage-9-5-lower-82 lean ejc-ds16-cages 86 86.0 82 82.0 cage-9-5 cage upper witness ejc-ds16-cages 96 96.0 cage-9-7 cage upper witness araujopardo-2010 1152 1152.0 cage-9-8 cage upper witness ejc-ds16-cages 1170 1170.0 cage-9-11 cage upper witness araujopardo-2010 74752 74752.0 74,752 cage-9-12 cage upper witness ejc-ds16-cages 74898 74898.0 74,898 cage-10-5 cage lower cage-10-5-lower-101 lean ejc-ds16-cages 103 103.0 101 101.0 cage-10-5 cage upper witness ejc-ds16-cages 124 124.0 cage-10-8 cage upper witness ejc-ds16-cages 1640 1640.0 cage-10-12 cage upper witness ejc-ds16-cages 132860 132860.0 132,860 cage-11-5 cage lower cage-11-5-lower-122 lean ejc-ds16-cages 124 124.0 122 122.0 cage-11-5 cage upper witness ejc-ds16-cages 154 154.0 cage-11-6 cage lower cage-11-6-lower-222 lean ejc-ds16-cages 224 224.0 222 222.0 cage-11-6 cage upper witness ejc-ds16-cages 240 240.0 cage-11-8 cage upper witness ejc-ds16-cages 2618 2618.0 cage-11-12 cage upper witness ejc-ds16-cages 319440 319440.0 319,440 cage-12-5 cage lower cage-12-5-lower-145 lean ejc-ds16-cages 147 147.0 145 145.0 cage-12-5 cage upper witness ejc-ds16-cages 203 203.0 cage-12-8 cage upper witness ejc-ds16-cages 2928 2928.0 cage-12-12 cage upper witness ejc-ds16-cages 354312 354312.0 354,312 cage-13-5 cage lower cage-13-5-lower-170 lean ejc-ds16-cages 174 174.0 170 170.0 cage-13-5 cage upper witness ejc-ds16-cages 230 230.0 cage-13-6 cage upper witness ejc-ds16-cages 336 336.0 cage-13-8 cage upper witness ejc-ds16-cages 4342 4342.0 cage-13-12 cage upper witness ejc-ds16-cages 738192 738192.0 738,192 cage-14-5 cage lower cage-14-5-lower-197 lean ejc-ds16-cages 199 199.0 197 197.0 cage-14-5 cage upper witness ejc-ds16-cages 288 288.0 cage-14-8 cage upper witness ejc-ds16-cages 4760 4760.0 cage-14-12 cage upper witness ejc-ds16-cages 804468 804468.0 804,468 cage-15-5 cage lower cage-15-5-lower-226 lean ejc-ds16-cages 230 230.0 226 226.0 cage-15-5 cage upper witness ejc-ds16-cages 312 312.0 cage-15-6 cage upper witness ejc-ds16-cages 462 462.0 cage-15-8 cage upper witness ejc-ds16-cages 7648 7648.0 cage-15-12 cage upper witness ejc-ds16-cages 1957376 1957376.0 1,957,376 cage-16-5 cage lower cage-16-5-lower-257 lean ejc-ds16-cages 259 259.0 257 257.0 cage-16-5 cage upper witness ejc-ds16-cages 336 336.0 cage-16-6 cage upper witness ejc-ds16-cages 504 504.0 cage-16-8 cage upper witness ejc-ds16-cages 8092 8092.0 cage-16-12 cage upper witness ejc-ds16-cages 2088960 2088960.0 2,088,960 cage-17-5 cage lower cage-17-5-lower-290 lean ejc-ds16-cages 294 294.0 290 290.0 cage-17-5 cage upper witness ejc-ds16-cages 448 448.0 cage-17-8 cage upper witness ejc-ds16-cages 8738 8738.0 cage-17-12 cage upper witness ejc-ds16-cages 2236962 2236962.0 2,236,962 cage-18-5 cage lower cage-18-5-lower-325 lean ejc-ds16-cages 327 327.0 325 325.0 cage-18-5 cage upper witness ejc-ds16-cages 480 480.0 cage-18-8 cage upper witness ejc-ds16-cages 10440 10440.0 10,440 cage-18-12 cage upper witness ejc-ds16-cages 3017196 3017196.0 3,017,196 cage-19-5 cage lower cage-19-5-lower-362 lean ejc-ds16-cages 364 364.0 362 362.0 cage-19-5 cage upper witness ejc-ds16-cages 512 512.0 cage-19-6 cage upper witness ejc-ds16-cages 720 720.0 cage-19-8 cage upper witness ejc-ds16-cages 13642 13642.0 13,642 cage-19-12 cage upper witness ejc-ds16-cages 4938480 4938480.0 4,938,480 cage-20-5 cage lower cage-20-5-lower-401 lean ejc-ds16-cages 403 403.0 401 401.0 cage-20-5 cage upper witness ejc-ds16-cages 576 576.0 cage-20-8 cage upper witness ejc-ds16-cages 14480 14480.0 14,480 cage-20-12 cage upper witness ejc-ds16-cages 5227320 5227320.0 5,227,320 van-der-waerden-2-3 van-der-waerden upper lean chvatal-1970 9 9.0 van-der-waerden-2-4 van-der-waerden upper lean chvatal-1970 35 35.0 van-der-waerden-2-5 van-der-waerden upper lean stevens-shantaram-1978 178 178.0 van-der-waerden-2-6 van-der-waerden upper lean kouril-paul-2011 1132 1132.0 van-der-waerden-3-3 van-der-waerden upper lean chvatal-1970 27 27.0 van-der-waerden-3-4 van-der-waerden upper lean kouril-2012 293 293.0 van-der-waerden-3-5 van-der-waerden lower witness rabung-lotts-2012 2174 2174.0 van-der-waerden-3-6 van-der-waerden lower witness rabung-lotts-2012 11192 11192.0 11,192 van-der-waerden-3-7 van-der-waerden lower witness rabung-lotts-2012 48812 48812.0 48,812 van-der-waerden-3-9 van-der-waerden lower witness rabung-lotts-2012 932746 932746.0 932,746 van-der-waerden-3-10 van-der-waerden lower witness rabung-lotts-2012 4173725 4173725.0 4,173,725 van-der-waerden-3-11 van-der-waerden lower witness rabung-lotts-2012 18603732 18603732.0 18,603,732 van-der-waerden-4-3 van-der-waerden upper lean beeler-oneil-1979 76 76.0 van-der-waerden-4-6 van-der-waerden lower witness monroe-2022 157349 157349.0 157,349 van-der-waerden-4-7 van-der-waerden lower witness monroe-2019 2284752 2284752.0 2,284,752 van-der-waerden-4-8 van-der-waerden lower witness monroe-2019 12288156 12288156.0 12,288,156 van-der-waerden-4-9 van-der-waerden lower witness monroe-2019 139847086 139847086.0 139,847,086 van-der-waerden-4-10 van-der-waerden lower witness monroe-2019 1189640579 1189640579.0 1,189,640,579 van-der-waerden-4-11 van-der-waerden lower witness monroe-2019 3464368084 3464368084.0 3,464,368,084 van-der-waerden-5-3 van-der-waerden lower witness rabung-lotts-2012 171 171.0 van-der-waerden-5-5 van-der-waerden lower witness komkov-2016 98742 98742.0 98,742 van-der-waerden-5-6 van-der-waerden lower witness monroe-2019 786741 786741.0 786,741 van-der-waerden-5-7 van-der-waerden lower witness monroe-2019 15993258 15993258.0 15,993,258 van-der-waerden-5-8 van-der-waerden lower witness monroe-2019 86017086 86017086.0 86,017,086 van-der-waerden-5-9 van-der-waerden lower witness monroe-2019 978929596 978929596.0 978,929,596 van-der-waerden-5-10 van-der-waerden lower witness monroe-2019 8327484047 8327484047.0 8,327,484,047 van-der-waerden-5-11 van-der-waerden lower witness monroe-2019 38108048914 38108048914.0 38,108,048,914 van-der-waerden-6-3 van-der-waerden lower witness blankenship-c-t-2018 226 226.0 van-der-waerden-6-5 van-der-waerden lower witness komkov-2016 98755 98755.0 98,755 van-der-waerden-6-6 van-der-waerden lower witness monroe-2019 1555550 1555550.0 1,555,550 van-der-waerden-6-7 van-der-waerden lower witness monroe-2019 111952800 111952800.0 111,952,800 van-der-waerden-6-8 van-der-waerden lower witness monroe-2019 602119596 602119596.0 602,119,596 van-der-waerden-6-9 van-der-waerden lower witness monroe-2019 6852507166 6852507166.0 6,852,507,166 van-der-waerden-6-10 van-der-waerden lower witness monroe-2019 58292388323 58292388323.0 58,292,388,323 van-der-waerden-6-11 van-der-waerden lower witness monroe-2019 419188538044 419188538044.0 419,188,538,044 circle-in-equilateral-7 circle-in-equilateral lower lean melissen-1993 2+4\sqrt{3} 8.928203 ≈8.928203 circle-in-equilateral-8 circle-in-equilateral lower lean melissen-1993 2+2\sqrt{3}+\frac{2\sqrt{33}}{3} 9.29381 ≈9.29381 circle-in-equilateral-9 circle-in-equilateral lower lean melissen-1993 6+2\sqrt{3} 9.464102 ≈9.464102 circle-in-equilateral-11 circle-in-equilateral lower lean melissen-1994a 4+2\sqrt{3}+\frac{4\sqrt{6}}{3} 10.73009 ≈10.73009 circle-in-equilateral-12 circle-in-equilateral lower lean melissen-1994b 4+4\sqrt{3} 10.9282 ≈10.9282 circle-in-equilateral-14 circle-in-equilateral lower lean payan-1997 8+2\sqrt{3} 11.4641 ≈11.4641 circle-in-equilateral-15 circle-in-equilateral lower lean oler-groemer-1961 8+2\sqrt{3} 11.4641 ≈11.4641 minimal-superpermutation-1 minimal-superpermutation lower lean trivial 1 1.0 minimal-superpermutation-2 minimal-superpermutation lower lean trivial 3 3.0 minimal-superpermutation-3 minimal-superpermutation lower lean egan-superpermutations 9 9.0 minimal-superpermutation-4 minimal-superpermutation lower lean egan-superpermutations 33 33.0 minimal-superpermutation-5 minimal-superpermutation lower lean chaffin-2014 153 153.0 minimal-superpermutation-6 minimal-superpermutation lower lean houston-pantone-vatter-2018 867 867.0 minimal-superpermutation-6 minimal-superpermutation upper minimal-superpermutation-6-upper-873 witness houston-2014 872 872.0 873 873.0 minimal-superpermutation-7 minimal-superpermutation lower lean houston-pantone-vatter-2018 5884 5884.0 minimal-superpermutation-7 minimal-superpermutation upper minimal-superpermutation-7-upper-5913 witness teodorescu-2026 5905 5905.0 5913 5913.0 minimal-superpermutation-8 minimal-superpermutation lower lean houston-pantone-vatter-2018 46085 46085.0 46,085 minimal-superpermutation-8 minimal-superpermutation upper witness egan-superpermutations 46205 46205.0 46,205 minimal-superpermutation-9 minimal-superpermutation lower lean houston-pantone-vatter-2018 408246 408246.0 408,246 minimal-superpermutation-9 minimal-superpermutation upper witness egan-superpermutations 408966 408966.0 408,966 affine-line-arrangements-1 affine-line-arrangements upper lean oeis-a241600-lines-on-plane 1 1.0 affine-line-arrangements-2 affine-line-arrangements upper lean oeis-a241600-lines-on-plane 2 2.0 affine-line-arrangements-3 affine-line-arrangements upper lean oeis-a241600-lines-on-plane 4 4.0 affine-line-arrangements-4 affine-line-arrangements upper lean oeis-a241600-lines-on-plane 9 9.0 affine-line-arrangements-5 affine-line-arrangements upper lean finschi-2001 47 47.0 affine-line-arrangements-6 affine-line-arrangements upper lean finschi-2001 791 791.0 affine-line-arrangements-7 affine-line-arrangements lower witness finschi-2001 37830 37830.0 37,830 affine-line-arrangements-7 affine-line-arrangements upper lean finschi-2001 37830 37830.0 37,830 affine-line-arrangements-8 affine-line-arrangements upper lean finschi-2001 4134940 4134940.0 4,134,940 affine-line-arrangements-general-position-1 affine-line-arrangements-general-position upper lean oeis-a090338-lines-on-plane-general 1 1.0 affine-line-arrangements-general-position-2 affine-line-arrangements-general-position upper lean oeis-a090338-lines-on-plane-general 1 1.0 affine-line-arrangements-general-position-3 affine-line-arrangements-general-position upper lean oeis-a090338-lines-on-plane-general 1 1.0 affine-line-arrangements-general-position-4 affine-line-arrangements-general-position upper lean oeis-a090338-lines-on-plane-general 1 1.0 affine-line-arrangements-general-position-5 affine-line-arrangements-general-position upper lean ringel-1956 6 6.0 affine-line-arrangements-general-position-6 affine-line-arrangements-general-position upper lean ringel-1956 43 43.0 affine-line-arrangements-general-position-7 affine-line-arrangements-general-position upper lean ringel-1956 922 922.0 affine-line-arrangements-general-position-8 affine-line-arrangements-general-position lower witness oeis-a090338-lines-on-plane-general 38609 38609.0 38,609 affine-line-arrangements-general-position-8 affine-line-arrangements-general-position upper lean oeis-a090338-lines-on-plane-general 38609 38609.0 38,609 affine-line-arrangements-general-position-9 affine-line-arrangements-general-position lower witness christ-2011 3111341 3111341.0 3,111,341 affine-line-arrangements-general-position-9 affine-line-arrangements-general-position upper lean christ-2011 3111341 3111341.0 3,111,341 golomb-ruler-1 golomb-ruler lower lean trivial 0 0.0 golomb-ruler-2 golomb-ruler lower lean trivial 1 1.0 golomb-ruler-3 golomb-ruler lower lean trivial 3 3.0 golomb-ruler-4 golomb-ruler lower lean trivial 6 6.0 golomb-ruler-5 golomb-ruler lower lean robinson-bernstein-1967 11 11.0 golomb-ruler-6 golomb-ruler lower lean robinson-bernstein-1967 17 17.0 golomb-ruler-7 golomb-ruler lower lean robinson-bernstein-1967 25 25.0 golomb-ruler-8 golomb-ruler lower lean mixon-1972 34 34.0 golomb-ruler-9 golomb-ruler lower lean mixon-1972 44 44.0 golomb-ruler-10 golomb-ruler lower lean mixon-1972 55 55.0 golomb-ruler-11 golomb-ruler lower lean mixon-1972 72 72.0 golomb-ruler-12 golomb-ruler lower lean robinson-1979 85 85.0 golomb-ruler-13 golomb-ruler lower lean robinson-1983 106 106.0 golomb-ruler-14 golomb-ruler lower lean shearer-1990 127 127.0 golomb-ruler-15 golomb-ruler lower lean shearer-1990 151 151.0 golomb-ruler-16 golomb-ruler lower lean shearer-1990 177 177.0 golomb-ruler-17 golomb-ruler lower lean sibert-1993 199 199.0 golomb-ruler-18 golomb-ruler lower lean sibert-1993 216 216.0 golomb-ruler-19 golomb-ruler lower lean dollas-rankin-mccracken-1998 246 246.0 golomb-ruler-20 golomb-ruler lower lean garry-vanderschel-1997 283 283.0 golomb-ruler-21 golomb-ruler lower lean garry-vanderschel-1998 333 333.0 golomb-ruler-22 golomb-ruler lower lean garry-vanderschel-1999a 356 356.0 golomb-ruler-23 golomb-ruler lower lean garry-vanderschel-1999b 372 372.0 golomb-ruler-24 golomb-ruler lower lean distributed-net-ogr-24 425 425.0 golomb-ruler-25 golomb-ruler lower lean distributed-net-ogr-25 480 480.0 golomb-ruler-26 golomb-ruler lower lean distributed-net-ogr-26 492 492.0 golomb-ruler-27 golomb-ruler lower lean distributed-net-ogr-27 553 553.0 golomb-ruler-28 golomb-ruler lower lean distributed-net-ogr-28 585 585.0 schur-1 schur upper lean trivial 1 1.0 schur-2 schur upper lean trivial 4 4.0 schur-3 schur upper lean trivial 13 13.0 schur-4 schur upper lean golomb-baumert-1965 44 44.0 schur-5 schur upper lean heule-2017-schur 160 160.0 schur-9 schur lower witness ageron-et-al-2021 17803 17803.0 17,803 weak-schur-1 weak-schur upper lean trivial 2 2.0 weak-schur-2 weak-schur upper lean trivial 8 8.0 weak-schur-3 weak-schur upper lean blanchard-harary-reis-2006 23 23.0 weak-schur-4 weak-schur upper lean blanchard-harary-reis-2006 66 66.0 weak-schur-7 weak-schur lower witness rowley-2020 2146 2146.0 weak-schur-8 weak-schur lower witness rowley-2020 6976 6976.0 weak-schur-9 weak-schur lower witness ageron-et-al-2021 22536 22536.0 22,536 snake-in-the-box-1 snake-in-the-box upper lean trivial 1 1.0 snake-in-the-box-2 snake-in-the-box upper lean davies-1965 2 2.0 snake-in-the-box-3 snake-in-the-box upper lean davies-1965 4 4.0 snake-in-the-box-4 snake-in-the-box upper lean davies-1965 7 7.0 snake-in-the-box-5 snake-in-the-box upper lean davies-1965 13 13.0 snake-in-the-box-6 snake-in-the-box upper lean davies-1965 26 26.0 snake-in-the-box-7 snake-in-the-box upper lean kochut-1996 50 50.0 snake-in-the-box-8 snake-in-the-box upper lean ostergard-pettersson-2014-snake 98 98.0 coil-in-the-box-2 coil-in-the-box upper lean kautz-1958 4 4.0 coil-in-the-box-3 coil-in-the-box upper lean kautz-1958 6 6.0 coil-in-the-box-4 coil-in-the-box upper lean kautz-1958 8 8.0 coil-in-the-box-5 coil-in-the-box upper lean kautz-1958 14 14.0 coil-in-the-box-6 coil-in-the-box upper lean davies-1965 26 26.0 coil-in-the-box-7 coil-in-the-box upper lean kochut-1996 48 48.0 coil-in-the-box-8 coil-in-the-box upper lean ostergard-pettersson-2014-coil 96 96.0