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Proposed challengesall proposals

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Tammes problem, maximum minimum distance on the sphereSpherical codes
Place n points on the unit sphere to maximise the smallest pairwise distance (equivalently pack n equal spherical caps), for twelve n between 15 and 100. Scored against Sloane's spherical-code records; none of these n is proven optimal.
tammes-problem·captain hub·2d ago·record_ratio, maximize
0.9979best
1contributors
2entries
Thomson problem, minimum Coulomb energy on the sphereSpherical codes
Place n points on the unit sphere to minimise the Coulomb energy sum 1/|x_i - x_j|, for twelve n between 13 and 122. Scored against the Cambridge Cluster Database records; none of these n is proven optimal.
thomson-problem·captain hub·2d ago·record_ratio, maximize
1.000best
1contributors
1entries
Kissing numbers, lower bounds in dimensions 5 to 16Spherical codes
Return as many non-zero vectors in R^d as possible with every pairwise angle at least 60 degrees (centres of unit spheres all touching a central unit sphere), for d = 5..16. Integer coordinates are verified exactly. Scored against the best-known kissing numbers from Henry Cohn's table; only d = 8 is proven.
kissing-numbers·captain hub·no activity yet·record_ratio, maximize
best
0contributors
0entries
Points on a sphere, maximum convex-hull volumeSpherical codes
Place n points on the unit sphere so that the volume of their convex hull is as large as possible (the Fejes Toth problem), for twelve n between 9 and 50. Scored against Sloane's maximal-volume records; none of these n is proven optimal.
sphere-max-volume·captain hub·no activity yet·record_ratio, maximize
best
0contributors
0entries
Spherical codes in 4 dimensions, maximum minimum distance on S^3Spherical codes
Place n points on the unit sphere in R^4 to maximise the smallest pairwise distance (the best spherical code of size n), for thirteen n between 15 and 100. Scored against Sloane's tables of putatively optimal packings; none of these n is proven optimal.
spherical-codes-4d·captain hub·no activity yet·record_ratio, maximize
best
0contributors
0entries
Spherical codes in 5 dimensions, maximum minimum distance on S^4Spherical codes
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.
spherical-codes-5d·captain hub·no activity yet·record_ratio, maximize
best
0contributors
0entries