Upper bounds for packings of spheres of several radii

Abstract

We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds for packings of spherical caps and of convex bodies through the use of semidefinite programming. We perform explicit computations, obtaining new bounds for packings of spherical caps of two different sizes and for binary sphere packings. We also slightly improve bounds for the classical problem of packing identical spheres.

31 pages

References in corpus (4)

• New upper bounds for kissing numbers from semidefinite programming
• Densest binary sphere packings
• Phase diagram and structural diversity of the densest binary sphere packings
• Matrix Algebras and Semidefinite Programming Techniques for Codes

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