No-three-in-line $D(65)$

130 points of the 65 by 65 grid with no three on a line

The largest number of points of the $65 \times 65$ grid with no three on a line.

Value: $130$ 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: $130$ Checked construction
no-three-in-line-65-lower-130, submitted by daniel-munro, 2026-11-05
[construction from M. Heule, personal communication, recorded on the no-three-in-line records page (2026-06-18).]
Upper bound: None yet

Updates from the literature

Upper bound: $130$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
2026-06-18 Lower bound: $130$
M. Heule, personal communication, recorded on the no-three-in-line records page (2026-06-18).
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]