Valid constraints for the Point Packing in a Square problem

We consider the problem of placing n$n$ points in the unit square in such a way as to maximize their minimum pairwise distance m$m$. Starting from two properties of the optimal solution presented by Locatelli and Raber in Discrete Applied Mathematics 122 (1–3) (2002) 139–166], and using the known theoretical lower and upper bounds, we derive some constraints for tightening the original formulation of the problem.