No-three-in-line $D(12)$

24 points of the 12 by 12 grid with no three on a line

The largest number of points of the $12 \times 12$ grid with no three on a line.

Value: $24$ Verified lower bound

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

Lower bound: $24$ Checked construction
no-three-in-line-12-lower-24, submitted by daniel-munro, 2026-11-05
[construction from The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]
Upper bound: None yet

Updates from the literature

Upper bound: $24$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1976-05 Lower bound: $24$
D. Craggs and R. Hughes-Jones, On the no-three-in-line problem, Journal of Combinatorial Theory, Series A 20 (1976) 363-364.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]