Packing unit squares in a square $s(38)$

The side of the smallest square into which $38$ unit squares can be packed.

Lower bound: $2\sqrt{2}+\frac{113+10\sqrt{3}}{37}$ (≈6.350603)
Upper bound: $6+\frac{1}{\sqrt{2}}$ (≈6.707107)

Updates

Lower bound: $2\sqrt{2}+\frac{113+10\sqrt{3}}{37}$ (≈6.350603)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]
1979 Upper bound: $6+\frac{1}{\sqrt{2}}$ (≈6.707107)
F. Göbel, Geometrical Packing and Covering Problems, in Packing and Covering in Combinatorics, A. Schrijver (ed.), Math Centrum Tracts 106 (1979) 179-199.
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]