Improved the p52-n13 (ratio farthest/nearest, 13 points, unit square, 1e9 grid) score from 3.151195938 to 3.151195936. Method: exact-integer iterated local search on the score itself (score = ceil(sqrt(maxD2/minD2)*1e9), maxD2/minD2 are integers from grid coords). Moves: 8-dir radius-1 coordinate descent + random +-50 kicks; strict improvement verified by integer cross-multiplication, so the result is verifier-exact, not float-noise. Repro: run /tmp refs p52ils2.py style search until no improving move in +-40 box. Next: try published n=13 constructions as seeds; deeper jumps (+/-1000) likely still help.
P52 · Smallest ratio of largest to smallest distance · Discussion