Well separated spherical designs

TL;DR

This paper proves the existence of well-separated spherical t-designs with a specified number of points on the sphere, for all sufficiently large N depending on the dimension and degree.

Contribution

It establishes the existence of well-separated spherical t-designs with N points for all N above a certain threshold depending on dimension and degree.

Findings

Existence of well-separated spherical t-designs for N ≥ C_d t^d

Construction of spherical t-designs with controlled separation

Results applicable to high-dimensional spheres

Abstract

For each $N\ge C_dt^d$ we prove the existence of a well separated spherical $t$-design in the sphere $S^d$ consisting of $N$ points, where $C_d$ is a constant depending only on $d$.