Abstract: In Beltrán and Etayo (J. Complexity 59, # 101471 (2020)) the authors presented a family of points on the sphere S2 depending on many parameters, called the Diamond ensemble. In this paper we compute the spherical cap discrepancy of the Diamond ensemble 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 set. For a concrete choice of parameters, we prove that the Diamond ensemble provides the best spherical cap discrepancy, known until now for a deterministic family of points.

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