New Upper Bounds on Sphere Packings I

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New Upper Bounds on Sphere Packings I

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Title: New Upper Bounds on Sphere Packings I
Author: Cohn, Henry; Elkies, Noam

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Citation: Cohn, Henry and Noam D. Elkies. 2003. New upper bounds on sphere packings I. Annals of Mathematics 157, no. 2: 689-714.
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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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