No-three-in-line $D(68)$

The largest number of points of the $68 \times 68$ 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: $136$ Checked construction
  no-three-in-line-68-lower-136, submitted by daniel-munro, 2026-11-05
  [construction from T. Prellberg, personal communication, recorded on the no-three-in-line records page (2026-03-23).]
• Upper bound: None yet

Updates from the literature

• Upper bound: $136$
  Trivial or easy according to the secondary source.
  [via No-three-in-line problem - Wikipedia]
• 2026-03-23 Lower bound: $136$
  T. Prellberg, personal communication, recorded on the no-three-in-line records page (2026-03-23).
  [via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]