Maximin Distance for n Points in a Unit Square or a Unit Circle

Abstract

Given n points inside a unit square (circle), let d _n (c _n ) denote the maximum value of the minimum distance between any two of the n points. The problem of determining d _n (c _n ) and identifying the configuration of that yields d _n (c _n ) has been investigated using geometric methods and computer-aided methods in a number of papers. We investigate the problem using a computer-aided search and arrive at some approximations which improve on earlier results for n=59, 73 and 108 for the unit square, and also for n=70, 73, 75 and 77, ⋯ , 80 for the unit circle. The associated configurations are identified for all the above-mentioned improved results.