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 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.