# 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?)