On a new method for constructing good point sets on spheres

Abstract

We use quadrature formulas with equal weights in order to construct N point sets on spheres in d-space (d ≥ 3) which are almost optimal with respect to a discrepancy concept, based on distance functions (potentials) and distance functionals (energies). By combining this approach with the probabilistic method, we obtain almost best possible approximations of balls by zonotopes, generated by N segments of equal length. © 1993 Springer-Verlag New York Inc.