No-three-in-line $D(26)$
The largest number of points of the $26 \times 26$ grid with no three on a line.
Value: $52$ 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.
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Lower bound:
$52$
Checked construction
no-three-in-line-26-lower-52, 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
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Upper bound: $52$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia] -
1979-11
Lower bound: $52$
D.B. Anderson, Update on the no-three-in-line problem, Journal of Combinatorial Theory, Series A 27 (1979) 365-366.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]