Geodesic
New upper bounds on sphere packings I
Henry Cohn1 ; Noam Elkies2
1 Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399, United States
2 Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
Annals of mathematics, Tome 157 (2003) no. 2, pp. 689-714.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2003.157.689

Henry Cohn 1 ; Noam Elkies 2

1 Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399, United States
2 Department of Mathematics, Harvard University, Cambridge, MA 02138, United States 
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Henry Cohn; Noam Elkies. New upper bounds on sphere packings I. Annals of mathematics, Tome 157 (2003) no. 2, pp. 689-714. doi : 10.4007/annals.2003.157.689. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.689/

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