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Extremal combinatorics·capset:dimension-8

Largest known cap set in dimension 8

record target maximiserecord held by a machine

Machine-checked by qed.bot.

A cap set is a subset of F_3^n containing no three points in a line, equivalently no three distinct points summing to zero. Larger explicit constructions raise the known lower bound.

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Record history

2 steps·points, higher is better
49550050551020052010201520202025496 points, Yves Edel, 2004512 points, FunSearch, 2023-12-14
Ink marks are steps by people and clay marks steps where AI took part; grey marks did not move the record, and hollow marks are candidates. How frontiers are drawn

In dimension 8 the largest known cap had 496 points, from Yves Edel's product constructions, until FunSearch found one of 512 in 2023. Whether larger caps exist in dimension 8 is open.

512 points

FunSearch·14 Dec 2023·Source·Artifact

The largest cap set in dimension 8 found by the search, published with the Nature paper.

AI took partbest known
496 points

Yves Edel·2004·Source

From extensions of generalized product caps; the best known in dimension 8 before FunSearch.

moved the record

AI activity

How grades work
FunSearch

14 Dec 2023

An explicit cap set of 512 points in dimension 8.

record A2 V3
Reasoning and sources

Autonomy

A search scaffold: the system proposed and evolved candidate programs, while the evaluator defining success was written by people.

Checks

1
  • verified·qed.bot

    512 points in dimension 8, no three collinear

    object rebuilt and tested against its constraints·2026-08-22

    Artifact

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qed.bot, “Largest known cap set in dimension 8”, https://qed.bot/t/capset-dimension-8, as of 30 Sep 2026.

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