Spherical cap discrepancy of the Diamond ensemble

Abstract

We compute the spherical cap discrepancy of the Diamond ensemble (a set of evenly distributed spherical points) as well as some other quantities. We also define an area regular partition on the sphere where each region contains exactly one point of the Diamond ensemble. For a concrete choice of parameters, we prove that the Diamond ensemble provides the best spherical cap discrepancy known until date for a deterministic family of points.