No-three-in-line $D(67)$

The largest number of points of the $67 \times 67$ grid with no three on a line.

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: $134$ Checked construction
  no-three-in-line-67-lower-134, submitted by daniel-munro, 2026-11-05
  [construction from M. Heule, personal communication, recorded on the no-three-in-line records page (2026-06-21).]
• Upper bound: None yet

Updates from the literature

• Upper bound: $134$
  Trivial or easy according to the secondary source.
  [via No-three-in-line problem - Wikipedia]
• 2026-06-21 Lower bound: $134$
  M. Heule, personal communication, recorded on the no-three-in-line records page (2026-06-21).
  [via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]