No-three-in-line $D(19)$

38 points of the 19 by 19 grid with no three on a line

The largest number of points of the $19 \times 19$ grid with no three on a line.

Value: $38$ 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: $38$ Checked construction
no-three-in-line-19-lower-38, 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: $38$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1988 Lower bound: $38$
H. Harborth, P. Oertel and T. Prellberg, No-three-in-line for seventeen and nineteen, Discrete Mathematics 73 (1988) 89-90.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]