Universal lower bounds for potential energy of spherical codes

Document Type


Presentation Date

Fall 10-14-2014

Conference Name

Minimal Energy Point Sets, Lattices, and Designs

Conference Location

Vienna, Austria


Erwin Schrodinger International Institute for Mathematical Physics

Peer Review



Based upon the works of Delsarte-Goethals-Seidel, Levenshtein, Yudin, and Cohn-Kumar we derive universal lower bounds for the potential energy of spherical codes, that are optimal (in the framework of the standard linear programming approach) over a certain class of polynomial potentials whose degrees are upper bounded via a familiar formula for spherical designs. We classify when improvements are possible employing polynomials of higher degree. Our bounds are universal in the sense of Cohn and Kumar; i.e., they apply whenever the potential is given by an absolutely monotone function of the inner product between pairs of points.


potential energy, spherical codes, universal configurations


Analysis | Discrete Mathematics and Combinatorics