Upper bounds for packings of spheres of several radII

Journal article (2014)
Department
Delft Institute of Applied Mathematics (EEMCS) (TU Delft)
Copyright: © The Author(s) 2014 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited
DOI: https://doi.org/doi:10.1017/fms.2014.24
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Published Date

23-09-2014

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Source:

Forum of Mathematics, Sigma, 2, (e23), 2014

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

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 the bounds for the classical problem of packing identical spheres.