A new upper bound for spherical codes

Naser T. Sardari, Masoud Zargar

Published 2020-01-01Version 1

We introduce a new linear programming method for bounding the maximum number $M(n,\theta)$ of points on a sphere in $n$-dimensional Euclidean space at an angular distance of not less than $\theta$ 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 $\delta_n$, the maximum packing density of an $n$-dimensional Euclidean space by equal balls.