“Packing Unit Squares in Squares: A Survey and New Results”, Erich Friedman2009-08-14 (math)⁠:

Let s(n) be the side of the smallest square into which we can pack n unit squares.

We present a history of this problem, and give the best known upper and lower bounds for s(n) for n ≤ 100, including the best known packings.

We also give relatively simple proofs for the values of s(n) when n = 2, 3, 5, 8, 15, 24, & 35, and more complicated proofs for n = 7 & 14. We also prove many other lower bounds for various s(n).