reference request – Upper bound of the maximum average distance between $n$ points in a $d$-dimensional ball for $dll log(n)$ and $ngg 1$

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?)