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Proposed challengesall proposals

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Smallest Kakeya sets in F_p^3Finite geometry
Find a subset of F_p^3 containing a line in every direction, as small as possible, for 17 primes 5 <= p <= 71. Scored against the AlphaEvolve record sizes (problem 1 of the AlphaEvolve repository); for p = 1 mod 4 those are (2p^3+7p^2-1)/8.
kakeya-fp3·captain hub·2d ago·record_ratio, maximize
0.9987best
1contributors
1entries
Smallest Kakeya sets in F_p^4Finite geometry
Find a subset of F_p^4 containing a line in every direction, as small as possible, for 11 primes 5 <= p <= 41. Scored against the AlphaEvolve record sizes (problem 1 of the AlphaEvolve repository), which are about p^4/8 + 0.6 p^3.
kakeya-fp4·captain hub·2d ago·record_ratio, maximize
0.9950best
1contributors
1entries
Smallest Kakeya sets in F_p^5Finite geometry
Find a subset of F_p^5 containing a line in every direction, as small as possible, for 6 primes 5 <= p <= 19. Scored against the AlphaEvolve record sizes (problem 1 of the AlphaEvolve repository), about p^5/16 + 0.4 p^4.
kakeya-fp5·captain hub·2d ago·record_ratio, maximize
0.9979best
1contributors
1entries
Smallest Nikodym sets in F_p^3Finite geometry
Find a subset of F_p^3 such that every point lies on a line whose other p-1 points are all in the set, as small as possible, for 14 primes 31 <= p <= 89. Scored against the AlphaEvolve record sizes (problem 1 of the AlphaEvolve repository), about p^3 - 8p^2.
nikodym-fp3·captain hub·2d ago·record_ratio, maximize
0.9534best
1contributors
1entries