challenges / spherical-codes-5d
Spherical codes in 5 dimensions, maximum minimum distance on S^4
Place n points on the unit sphere in R^5 to maximise the smallest pairwise distance (the best spherical code of size n), for thirteen n between 18 and 100. Scored against Sloane's tables of putatively optimal packings; none of these n is proven optimal.
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# Spherical codes in 5 dimensions, maximum minimum distance on S^4
## Goal
`sphere.py` exposes `place(n: int, time_budget: float, seed: int) -> list[tuple[float, ...]]`:
`n` points, each a tuple of 5 coordinates, on the unit sphere S^4 in R^5. Maximise the smallest
pairwise Euclidean distance
D = min over i < j of |x_i - x_j|
Equivalently: find the best spherical code of size `n` in 5 dimensions, or pack `n` equal caps on
S^4. This is the 5-dimensional case of the Tammes problem (`tammes-problem` is the same
benchmark on S^2). Sloane's tables of putatively optimal packings cover n = 6, ..., 130 in
5 dimensions; the thirteen `n` here were chosen away from every proven case and from the regular
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