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Three-point bounds for sphere packing

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arxiv 2206.15373 v1 pith:WCY4XECE submitted 2022-06-30 math.MG

Henry Cohn , David de Laat , Andrew Salmon This is my paper · ORCID
classification math.MG
keywords boundspackingthree-pointboundspheredimensionprogrammingchoosing
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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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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Linear Programming Bounds for Fibered Sphere Packings

    math.MG 2026-07 conditional novelty 8.0 of 10

    Linear programming bounds are sharp for some fibered sphere packings, collapse to the planar bound in a key six-dimensional case, and fail to prove the Cohn–Rajagopal conjecture for D5/A3.

  2. A Three-Point Continuous-Variable Quantum MacWilliams Identity

    quant-ph 2026-07 conditional novelty 8.0 of 10

    A three-point continuous-variable quantum MacWilliams identity is constructed, and shown to collapse exactly to the two-point bound for GKP lattice and certifiable bosonic code sectors.

  3. On two counterexamples in the geometry of numbers

    math.MG 2026-07 conditional novelty 8.0 of 10

    Rotated E8 yields a strict lattice packing density gain for the product of two 4-balls over D4×D4, and a one-parameter deformation of the densest 9-dimensional lattice lowers its spectral height.

  4. Continuous-Variable Quantum MacWilliams Identities

    quant-ph 2025-02 conditional novelty 7.0 of 10

    Continuous-variable quantum MacWilliams identities yield quantum Cohn-Elkies and Levenshtein bounds, and conditional optimality of E8/Leech GKP codes.

  5. A dual linear programming bound for sphere packing in dimension 36

    math.MG 2026-07 conditional novelty 6.0 of 10

    In dimension 36, a modular-form certificate proves the Cohn–Elkies LP bound exceeds the density of the best known packing by at least a factor of 32.9.

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