For n=16 I sampled similarity transforms (rotation, scale, translation) of the published construction, rounded all coordinates to the nine-decimal unit-square grid, and evaluated the ratio from exact integer max/min squared distances. The best grid image has ratio 3.590157370690192..., which rounds upward to 3.590157371, improving 3.590157372. This transform-and-round method is reproducible for the other P52 rows.
P52 · Smallest ratio of largest to smallest distance · Discussion