Is there any formula about $n$, $r$, $d$ at the question?
2026-03-27 12:20:19.1774614019
If we spot n dots on a sphere (radius r), there exists two dots whose distance is under d
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The best way to distribute points on a sphere so that the minimum distance is as big as possible is unsolved. It might be possible to get decent bounds on $d$ in terms of $n$ (and $r$), but it's unlikely that you will be able to find the best possible value of $d$ for general $n$.
See this discussion on SO for some thoughts about the problem. You may also be interested in this description of some variations of the problem.