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arXiv · 2206.15373

Three-point bounds for sphere packing

Henry Cohn·David de Laat·Andrew Salmon
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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.

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Henry Cohn, David de Laat, Andrew Salmon. 2022-06-30. Three-point bounds for sphere packing. https://arxiv.org/abs/2206.15373

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