QMC strength for some random configurations on the sphere

Abstract

A sequence $(X_N)\subset {\mathbb{S}}^d$ of N-point sets from the d-dimensional sphere has QMC strength $s^{\ast }>d/2$ if it has worst-case error of optimal order, $N^{s/d}$, for Sobolev spaces of order $s$ for all $d/2<s<s^{\ast }$ , and the order is not optimal for $s>s^{\ast }$ . In arXiv:1208.3267 conjectured values of the strength are given for some well known point families in ${\mathbb{S}}^2$ based on numerical results. We study the average QMC strength for some related random configurations.