From: Dave Rusin <rusin@math.niu.edu>
Date: Fri, 13 Nov 1998 11:08:22 -0600 (CST)
To: maurice_clerc@my-dejanews.com
Subject: Re: Optimal distribution of N points
Newsgroups: sci.math

This is a hard question, even in 2-dimensional space. There is some
difficulty in deciding what "optimal" means, but even with a well-defined
criterion there is no clear way to find the best distribution.
If the number of points N is really large relative to  D, I'd observe
that I want roughly a   k x k x ... x k  grid, where  k^D = N. So let
k1=round(N^(1/D)), and then put points with x1-coordinate only a multiple
of  1/k1. You want roughly  N/k1  points with each of those  x1-coordinates;
let N1_1=round(N/k1), N1_2 = round((N-N1_1)/(k1-1)), 
N1_3=round((N-N1_1-N1_2)/(k1-2)), etc.  Then for each  i  from 1 to  k1, you
need only arrange  N1_i  points in the unit box in  (D-1)-dimensional space.
So arrange this in a recursive computer algorithm.

There are references to this in Guy's "Unsolved Problems in Geometry".
You can get some other references, including links to Sloane's useful site,
from
	index/spheres.html
where the focus is on the related problem of arranging points around a 
_sphere_ instead of a box.

dave