QMC Strength for Some Random Configurations on the Sphere

A sequence \((X_N)\subset \mathbb {S}^d\) of N-point sets from the d-dimensional sphere has QMC strength \(s^*>d/2\) if it has worst-case error of optimal order, \(N^{-s/d},\) for Sobolev spaces of order s for all \(d/2<s_s_ and="" the="" order="" is="" not="" optimal="" for="" _s=""> s^*.\) In [15] 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.