Three-point bounds for sphere packing
Metric Geometry
2022-07-01 v1
Abstract
We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a truncation radius for the three-point function. As a result, we obtain new upper bounds on the sphere packing density in dimension 4 through 7 and 9 through 16. We also give a different three-point bound for lattice packing and conjecture that this second bound is sharp in dimension 4.
Cite
@article{arxiv.2206.15373,
title = {Three-point bounds for sphere packing},
author = {Henry Cohn and David de Laat and Andrew Salmon},
journal= {arXiv preprint arXiv:2206.15373},
year = {2022}
}
Comments
37 pages, 1 figure