Year: 2022
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Cohn, Henry, de Laat, David, Salmon, Andrew
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4283782673