New upper bounds on sphere packings I

Henry Cohn, Noam Elkies

Published 2001-10-01, updated 2003-09-03Version 3

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.