# N 3d integer points in box with maximum average distance

given a 3d cube with a size of m x m x m, is there an efficient algorithm to find N integer points with the average Euclidean distance between each pair maximized? If not, is there any evolutionary approach I can take to this, so in each step the solution will be improved?

Thanks!

• You'll get a pretty good solution if you choose $N$ points at random. – Yuval Filmus May 9 at 9:04

• 1. For 5 points, it appears you are assuming that it is optimal to place 4 of the points in a corner. What if there is a better solution that does not involve having at least 4 points in a corner? 2. For cubes, you propose a solution when $N$ is a multiple of 8. How do you know that it is optimal, and that there is no better solution? – D.W. May 9 at 21:29