Cohn, HenryElkies, Noam2009-05-192003Cohn, Henry and Noam D. Elkies. 2003. New upper bounds on sphere packings I. Annals of Mathematics 157, no. 2: 689-714.0003-486Xhttp://nrs.harvard.edu/urn-3:HUL.InstRepos:2960190We 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.en-US10.4007/annals.2003.157.689