A new upper bound for spherical codes

01/01/2020

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by   Naser T. Sardari, et al.

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We introduce a new linear programming method for bounding the maximum number M(n,θ) of points on a sphere in n-dimensional Euclidean space at an angular distance of not less than θ from one another. We give the unique optimal solution to this linear programming problem and improve the best known upper bound of Kabatyanskii and Levenshtein. By well-known methods, this leads to new upper bounds for δ_n, the maximum packing density of an n-dimensional Euclidean space by equal balls.