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New upper bounds on sphere packings I

Henry Cohn·Noam Elkies
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Abstract

We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.

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Henry Cohn, Noam Elkies. 2003-09-03. New upper bounds on sphere packings I. https://doi.org/10.4007/annals.2003.157.689

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