We have a sphere of radius $r$ in a $d$-dimensional space. What is the maximum amount of points that I can fit inside the sphere such as the distance between any pair of points is at least $r$? And strictly bigger than $r$?
I believe this is equivalent to packing d-dimensional spheres of radius r/2 inside a sphere of radius r.
If you have an idea on the order of the answer I would also appreciate it.
This question says that the number is 12 for d=3, what about for a general d?
As opposed to this question, I'm only concerned for points at distance $r$, not any arbitrary distance.