Let $S_n$ be the set of $n$ points belonging to a $d$-dimensional unit ball, where $dll log(n)$. Let $d_n$ be the *average* distance between *any* two distinct points of $S_n$.

**Question:** How can we find a (*tight if possible*) upper bound of the maximum value $d^*_n$ of $d_n$ over all possible sets $S_n$, when $ngg 1$?

(*Is this problem related to placing $n$ points on a unit $(d-1)$-sphere maximizing the minimum distance between any two of them?*)