I would like to know if there is an explicit formula to determine, for a fix integer $N>1$, the supremum among $N$ points inside the unit disk $D$, of their minimum distance:
$d(N)=\sup_{\{x_1,\dots,x_N\}\subset D}\min_{1\le j<k\le N}|x_j-x_k|$
First values of $N$ are easy, but things become more elaborated as $N$ grows. Maybe there is an asymptotic expression as $N$ tends to infinity?
Thanks!