TheD4Root System Is Not Universally Optimal

DOI10.1080/10586458.2007.10129008zbMath1137.05020arXivmath/0607447OpenAlexW2094544653MaRDI QIDQ5449055

Noam D. Elkies, Conway, John H., Abhinav Kumar, Henry Cohn

Publication date: 10 March 2008

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607447

zbMATH Keywords

spherical designspherical code24-celluniversally optimal codepotential energy minimization\(D_4\) root system

Mathematics Subject Classification ID

Decoding (94B35) Combinatorial aspects of packing and covering (05B40)

Related Items (15)

Design theory from the viewpoint of algebraic combinatorics ⋮ Optimal asymptotic bounds for spherical designs ⋮ Three-point bounds for energy minimization ⋮ Spherical designs and modular forms of the \(D_4\) lattice ⋮ On polarization of spherical codes and designs ⋮ Efficient Spherical Designs with Good Geometric Properties ⋮ Upper energy bounds for spherical designs of relatively small cardinalities ⋮ Universal lower bounds on energy and LP-extremal polynomials for \((4, 24)\)-codes ⋮ Towards a proof of the 24-cell conjecture ⋮ Universal lower bounds for potential energy of spherical codes ⋮ Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets ⋮ A survey on spherical designs and algebraic combinatorics on spheres ⋮ Universally optimal distribution of points on spheres ⋮ Majorization and Minimal Energy on Spheres ⋮ Bounds for spherical codes: The Levenshtein framework lifted

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