No-three-in-line $D(41)$

82 points of the 41 by 41 grid with no three on a line

The largest number of points of the $41 \times 41$ grid with no three on a line.

Value: $82$ 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: $82$ Checked construction
no-three-in-line-41-lower-82, 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: $82$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1998-01 Lower bound: $82$
A. Flammenkamp, Progress in the no-three-in-line problem, II, Journal of Combinatorial Theory, Series A 81 (1998) 108-113.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]