New upper bounds on sphere packings I

2003/03/01 by Henry Cohn, Noam Elkies, Noam D. Elkies · 16 citations
Mathematics · Engineering · Computer Science · #Mathematical Approximation and Integration #graph theory and CDMA systems #Computational Geometry and Mesh Generation

paper · pdf · doi:10.4007/annals.2003.157.689

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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• A Riemannian Variational and Spectral Framework for High-Dimensional Sphere Packing: Barrier-Dynamics Reconciliation, Periodic Rigidity, and Discrete-Time Guarantees
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