10th Summer School in Potential Theory
We derive universal lower bounds for the potential energy of spherical codes, that are optimal in the framework of Delsarte-Yudin linear programming method. Our bounds are universal in the sense of both Levenshtein and Cohn-Kumar; i.e., they are valid for any choice of dimension and code cardinality and they apply to any absolutely monotone potential. We further discuss a characterization on when the lower bounds are LP-optimal, that is they are the best possible in terms of the linear programming approach. Finally, we present the analogous results for codes in projective spaces.
potential energy, spherical codes, universal configurations
Analysis | Discrete Mathematics and Combinatorics | Other Physical Sciences and Mathematics
Peter D. Dragnev, Peter Boyvalenkov, Douglas P. Hardin, Edward B. Saff, and Maya Stoyanova (2015).
Energy bounds for spherical codes, test functions and LP optimality. Presented at 10th Summer School in Potential Theory, Budapest, Hungary.