New upper bounds on sphere packings I

Henry Cohn, Noam D. Elkies

Type: Article

Publication Date: 2003-03-01

Citations: 306

DOI: https://doi.org/10.4007/annals.2003.157.689

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.

Locations

arXiv (Cornell University) - View - PDF
Digital Access to Scholarship at Harvard (DASH) (Harvard University) - View - PDF
DataCite API - View
Annals of Mathematics - View - PDF

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