New results in the packing of equal circles in a square

The problem of finding the maximum diameter of n equal mutually disjoint circles inside a unit square is addressed in this paper. Exact solutions exist for only n = 1, ..., 9,10,16,25,36 while for other n only conjectural solutions have been reported. In this work a max-min optimization approach is introduced which matches the best reported solutions in the literature for all n ≤ 30, yields a better configuration for n = 15, and provides new results for n = 28 and 29.