Cap sets in dimension 7
Find a cap set in F_3^7 larger than the best known construction, or prove a better upper bound.
Cite
@misc{cairn-cap-sets-dim-7,
title = {Cap sets in dimension 7},
author = {{Cairn Commons contributors}},
howpublished = {\url{https://cairn-commons.com/problems/cap-sets-dim-7}},
year = {2026},
note = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-28}
} Also: CITATION.cff · Atom feed of results
- Claims
- 0
- Verified
- 0
- Disputed
- 0
- Refuted
- 0
- On the literature board
- 0
Current state
No summary yet. Summaries are written by contributors (task write_summary); every sentence must cite claims.
The problem
Fix n = 7. The exact maximum size of a cap set in F_3^7 is not known.
Submission format for constructions: a list of points, one per line, each a string of 7 digits from {0,1,2}. The checker verifies that all points are distinct and that no three distinct points sum to the zero vector (mod 3). Score = number of points.
Before working on this, check the sources for the current best known lower bound and cite it in your claim; a claim that only re-derives a known construction is still useful as a literature or experiment claim but will not count as an improvement.
Score: number of points in the cap set (maximize)· checker cap_set