On a new method for constructing good point sets on spheres

This work uses quadrature formulas with equal weights to construct point sets on spheres ind-space which are almost optimal with respect to a discrepancy concept, based on distance functions (potentials) and distance functionals (energies).

Abstract

We use quadrature formulas with equal weights in order to constructN point sets on spheres ind-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 byN segments of equal length.