Upper bounds for packings of spheres of several radii

DOI10.1017/fms.2014.24zbMath1310.52022arXiv1206.2608OpenAlexW2115967956WikidataQ56267765 ScholiaQ56267765MaRDI QIDQ5496785

David de Laat, Frank Vallentin, Fernando Mário de Oliveira Filho

Publication date: 28 January 2015

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.2608

zbMATH Keywords

convex bodiespacking problemsspherical capsdensities of packingslinear programming upper bounds

Mathematics Subject Classification ID

Semidefinite programming (90C22) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

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Uses Software

• SageMath

Cites Work

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• Real zeros for positive semidefinite forms. I
• Optimality and uniqueness of the Leech lattice among lattices
• Lower bounds for measurable chromatic numbers
• Ausfüllung der Ebene durch Kreise
• The ellipsoid method and its consequences in combinatorial optimization
• Spherical codes and designs
• Some densest two-size disc packings in the plane
• New upper bounds on sphere packings. I
• Packing of incongruent circles on the sphere
• Remarks on my paper: ``Packing of incongruent circles on the sphere
• A proof of the Kepler conjecture
• Positive definite functions on spheres
• The Packing of Equal Spheres
• Universally optimal distribution of points on spheres
• New upper bounds for kissing numbers from semidefinite programming
• High-Accuracy Semidefinite Programming Bounds for Kissing Numbers
• A Survey of Condition Number Estimation for Triangular Matrices
• Pre- and Post-Processing Sum-of-Squares Programs in Practice
• Integer Decomposition for Polyhedra Defined by Nearly Totally Unimodular Matrices
• On linear unequal error protection codes
• Packing circles of two different sizes on the sphere. II
• Random heterogeneous materials. Microstructure and macroscopic properties