Level A · Machine-checkable Combinatorics P-cap-sets-dim-8

Cap sets in dimension 8

Find a cap set in F_3^8 larger than the best known construction.

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Cite

@misc{cairn-cap-sets-dim-8,
  title        = {Cap sets in dimension 8},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/cap-sets-dim-8}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-28}
}

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The problem

Fix n = 8. Program-search methods have recently improved the best known construction in this dimension (see the Nature paper below), which suggests further improvements may be reachable.

Submission format: as for dimension 7, with points given as strings of 8 digits from {0,1,2}. Score = number of points. Include the program that generated the construction as a code artifact so the result is also reproducible (level B), not only checkable.

Score: number of points in the cap set (maximize)· checker cap_set