Bounds on three- and higher-distance sets
Combinatorics
2011-08-24 v2
Abstract
A finite set X in a metric space M is called an s-distance set if the set of distances between any two distinct points of X has size s. The main problem for s-distance sets is to determine the maximum cardinality of s-distance sets for fixed s and M. In this paper, we improve the known upper bound for s-distance sets in n-sphere for s=3,4. In particular, we determine the maximum cardinalities of three-distance sets for n=7 and 21. We also give the maximum cardinalities of s-distance sets in the Hamming space and the Johnson space for several s and dimensions.
Cite
@article{arxiv.1005.2639,
title = {Bounds on three- and higher-distance sets},
author = {Oleg R. Musin and Hiroshi Nozaki},
journal= {arXiv preprint arXiv:1005.2639},
year = {2011}
}
Comments
12 pages