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Three-point bounds for sphere packing

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.

preprint2022arXivOpen access
Henry CohnDavid de LaatAndrew Salmon
math.MG
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Open access3 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Henry CohnDavid de LaatAndrew Salmon

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