I am trying to pick the $n$ most distant colors from each other to make the most varied palette possible. Since the most commonly used color space (RGB) is a cube, this means I need to know the $n$ most distant points on that cube.
By most distant points, I mean that the two closest points have as high a distance between them as possible.
For $n = 2 \lor 3 \lor 4 \lor 8 \lor 9$, the answers are simple, but for other $n$ there seems to be no obvious way to calculate them apart from brute force computation.