I would like to know if there is a formula, or at least some bounds, for the following problem. Consider a (three-dimensional) sphere of radius R. What is the maximum number of equal spheres, all of radius $r<R$, that I can put on the surface of the large sphere without having the small spheres overlap? The arrangement need not be regular. That is, the requirements are 1. that the centers of the small spheres are all at $R+r$ from the center of the large central sphere; and 2. that the centers of the small spheres are at least $2r$ apart from each other.
I have googled quite a bit and came across various papers about the kissing number (which is a more restricted problem) and spherical codes, but if I understand it correctly, the latter is not quite the problem I consider, because the minimum distance is to be maximized rather than minimized.