I assume that this sort of question has already been considered at great length. Nevertheless, I could not find an answer to this question in the related literature.

Given a constant $a\in (0,2]$, what are the known upper bounds of the maximum number of points we can place on the $d$-dimensional unit sphere such that the Euclidean distance between any two of them is larger or equal to $a$, for $d\gg 1$?