No-three-in-line $D(34)$

68 points of the 34 by 34 grid with no three on a line

The largest number of points of the $34 \times 34$ grid with no three on a line.

Value: $68$ 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: $68$ Checked construction
no-three-in-line-34-lower-68, 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: $68$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1992-07 Lower bound: $68$
A. Flammenkamp, Progress in the no-three-in-line problem, Journal of Combinatorial Theory, Series A 60 (1992) 305-311.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]