TITLE: well separated points on sphere
QUESTION [14 upvotes]: Is there a way to generate k points on a n-sphere, say, $x_1,\dots,x_k$ such that $\min_{ i \neq j } \| x_i - x_j \| $ is as large as possible? Approximate solutions are also OK, I just need well separated points on a sphere.

REPLY [2 votes]: There are lots of papers for nearly uniform distribution of points on 2-sphere, however, the question is for general n-sphere, for which the only systematic way I have seen is Fisher's 1986 PVQ: pyramid vector quantizer, used in data compressors e.g. OPUS audio codec.
It starts with uniform point distribution on l1 sphere ("pyramid"): set of integer points of fixed sum of absolute values. Then projects these points to l2 sphere. To get more uniform point distribution we can use some deformation like power before the projection.