# New upper bounds on sphere packings I

### 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.

## Authors

Henry Cohn

Microsoft Research
One Microsoft Way
Redmond, WA 98052-6399
United States

Noam Elkies

Department of Mathematics
Harvard University
Cambridge, MA 02138
United States