Work

Dual linear programming bounds for sphere packing via modular forms

Year: 2021

Type: article

Abstract: We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions 8 8 and 24 24 , where the linear programming bound is sharp, we show that it comes nowhere near the best packing densities known in dimensions 12 12 , 16 16 , 20 20 , 28 28 , and 32 32 . More generally, we provide a systematic technique for proving separations of this sort.

Source: Mathematics of Computation

DOI: 10.1090/mcom/3662

Authors: Henry Cohn, Nicholas Triantafillou

Institutions: Microsoft Research New England (United States), University of Georgia, Massachusetts Institute of Technology

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation, Microsoft Research