Some previous questions (here and here) ask for algorithms to place $N$ points evenly on the $d$-dimensional unit sphere. In my case, what I am looking for is that, given these $N$ points that are evenly placed on the $d$-dimensional unit sphere (the center of the sphere is the origin in $\mathbb{R}^d$), I want to approximate/bound the angle of two closest points among such $N$ points. When $d=2$, this angle is $2 \pi / N$. Is there any similar result/approximation for $d > 2$? I would be grateful for hints or pointers to relevant results.

Thank you everyone for your time.