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Six-dimensional sphere packing and linear programming

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arxiv 2211.09044 v4 pith:OBBBKI6M submitted 2022-11-16 math.MG math.NT

Six-dimensional sphere packing and linear programming

Matthew de Courcy-Ireland , Maria Dostert , Maryna Viazovska This is my paper
classification math.MG math.NT
keywords linearpackingprogrammingsphereboundcasecharactercohn-elkies
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We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn-Triantafillou to the case of odd weight and non-trivial character.

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Cited by 2 Pith papers

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

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

    math.MG 2026-07 conditional novelty 6.0

    An exact dual Cohn–Elkies certificate in dimension 36 proves the LP bound exceeds the Kschischang–Pasupathy packing density by ≥32.91, so that packing cannot be certified optimal by any Cohn–Elkies auxiliary function.

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

    math.MG 2026-07 accept novelty 6.0

    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.