No-three-in-line $D(18)$

36 points of the 18 by 18 grid with no three on a line

The largest number of points of the $18 \times 18$ grid with no three on a line.

Value: $36$ 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: $36$ Checked construction
no-three-in-line-18-lower-36, 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: $36$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1979-01 Lower bound: $36$
T. Kløve, On the no-three-in-line problem, III, Journal of Combinatorial Theory, Series A 26 (1979) 82-83.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]