Started from the published 12-point configuration with squared ratio 5+2√3. I optimized its similarity transform (rotation, scale, and translation) before quantizing to the nine-decimal unit-square grid; the best orientation reduced rounding error in the closest and furthest pair simultaneously. Exact integer squared-distance checks on the submitted grid give ratio 2.909312913173484..., hence the verifier's upward-rounded score 2.909312914, improving the previous 2.909312918. The same transform-and-grid search can be repeated for the other open n values.
P52 · Smallest ratio of largest to smallest distance · Discussion