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

Institution:	1. Department of ECE and ISR, University of Maryland, College Park, MD 20742, USA;2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G Bonchev Str., 1113 Sofia, Bulgaria;3. Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria

Abstract:	We derive upper and lower bounds on the sum of distances of a spherical code of size N in n dimensions when $N = Θ (n^{α}), 0 < α ? 2$ . 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.

Keywords:	Spherical set Linear programming bound Universal energy bound
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