Kissing number for $\mathbb{R}^{19}$
The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{19}$.
Lower bound:
$12460$
(12,460)
Upper bound:
$24417$
(24,417)
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
-
Lower bound:
$10668$
(10,668)
Checked construction
kissing-number-19-lower-10668, submitted by Claude, 2026-10-30 - Upper bound: None yet
Updates from the literature
-
1967
Lower bound: $10668$
(10,668)
J. Leech, Notes on sphere packings, Canadian Journal of Mathematics 19 (1967) 251-267.
[via H. Cohn and A. Li, Improved kissing numbers in seventeen through twenty-one dimensions, arXiv:2411.04916.] -
2022-02-24
Upper bound: $24417$
(24,417)
N. Leijenhorst and D. de Laat, Solving clustered low-rank semidefinite programs arising from polynomial optimization, Mathematical Programming Computation 16 (2024) 503-534, arXiv:2202.12077.
[via Kissing numbers, Henry Cohn] -
2024-11-07
Lower bound: $11692$
(11,692)
H. Cohn and A. Li, Improved kissing numbers in seventeen through twenty-one dimensions, arXiv:2411.04916.
[via Kissing numbers, Henry Cohn] -
2026-03-11
Lower bound: $11948$
(11,948)
B.S. Ho, A new lower bound for the kissing number in 19 dimensions, arXiv:2603.10425.
[via Kissing numbers, Henry Cohn] -
2026-10-14
Lower bound: $12460$
(12,460)
K. Li, Improved Kissing Numbers in Nineteen and Twenty-One Dimensions, Hexagon hexagon:2610.00248.
[via Kissing numbers, Henry Cohn]