No-three-in-line $D(23)$

46 points of the 23 by 23 grid with no three on a line

The largest number of points of the $23 \times 23$ grid with no three on a line.

Value: $46$ 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: $46$ Checked construction
no-three-in-line-23-lower-46, 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: $46$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1990 Lower bound: $46$
Gerken, personal communication to H. Harborth (1990), cited on the no-three-in-line records page.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]