Hyperuniform point sets on the sphere: deterministic constructions

TL;DR

This paper extends the concept of hyperuniformity to spheres of any dimension and demonstrates that QMC-designs, including spherical designs, exhibit hyperuniformity in this generalized sense.

Contribution

It introduces a generalized definition of hyperuniformity on spheres and proves that QMC-designs are hyperuniform under this new framework.

Findings

QMC-designs are hyperuniform on spheres of arbitrary dimension

Spherical designs satisfy the hyperuniformity criteria

The generalized hyperuniformity concept applies broadly to spherical point sets

Abstract

We study a generalisation of the concept of hyperuniformity to spheres of arbitrary dimension. It is shown that QMC-designs (and especially spherical designs) are hyperuniform in our sense.