Packing unit squares in a square $s(51)$

The side of the smallest square into which $51$ unit squares can be packed.

Lower bound: $2\sqrt{2}+\frac{101+3\sqrt{14}}{25}$ (≈7.317426)
Upper bound: ${\approx}7.7044$

Updates

Upper bound: ${\approx}7.7044$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]
Lower bound: $2\sqrt{2}+\frac{101+3\sqrt{14}}{25}$ (≈7.317426)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]