SPHERICAL CAP DISCREPANCY
OF THE DIAMOND ENSEMBLE

The spherical cap discrepancy of a set of points on the unit sphere compares the number of points falling on a spherical cap with its normalized Lebesgue measure.

One fundamental open problem in uniform distribution theory consists on finding explicit sequences of configurations of points with the minimal spherical cap discrepancy possible. For deterministic families of points the problem is still open.

In this article we provide asymptotic upper and lower bounds for the discrepancy of the Diamond ensemble, a deterministic family of points on the unit sphere.

Based on a paper by Ujué Etayo.

Published in Discrete & Computational Geometry.

DOI: https://doi.org/10.1007/s00454-021-00305-4