No-three-in-line $D(3)$

6 points of the 3 by 3 grid with no three on a line

The largest number of points of the $3 \times 3$ grid with no three on a line.

Value: $6$ 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: $6$ Checked construction
no-three-in-line-3-lower-6, 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: $6$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1975-05 Lower bound: $6$
R.R. Hall, T.H. Jackson, A. Sudbery and K. Wild, Some advances in the no-three-in-line problem, Journal of Combinatorial Theory, Series A 18 (1975) 336-341.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]