Packing unit squares in a square $s(26)$

The side of the smallest square into which $26$ unit squares can be packed.

Lower bound: $2\sqrt{2}+\frac{27+2\sqrt{10}}{13}$ (≈5.391854)
Upper bound: $\frac{7}{2}+\frac{3\sqrt{2}}{2}$ (≈5.62132)

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