No-three-in-line $D(13)$

26 points of the 13 by 13 grid with no three on a line

The largest number of points of the $13 \times 13$ grid with no three on a line.

Value: $26$ 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: $26$ Checked construction
no-three-in-line-13-lower-26, 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: $26$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1977-03 Lower bound: $26$
M. Gardner, Mathematical Games, Scientific American 236 (March 1977) 139-140.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]