Bounds for the sum of distances of spherical sets of small size

Alexander Barg; Peter Boyvalenkov; Maya Stoyanova

doi:10.1016/j.disc.2023.113346

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arXiv · 2105.03511

Bounds for the sum of distances of spherical sets of small size

Alexander Barg·Peter Boyvalenkov·Maya Stoyanova

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Abstract

We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical sets. We discuss asymptotic behavior of our bounds along with several examples of codes whose sum of distances closely follows the upper bound.

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BibTeX RIS

Alexander Barg, Peter Boyvalenkov, Maya Stoyanova. 2021-05-07. Bounds for the sum of distances of spherical sets of small size. https://doi.org/10.1016/j.disc.2023.113346

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