No-three-in-line $D(8)$

16 points of the 8 by 8 grid with no three on a line

The largest number of points of the $8 \times 8$ grid with no three on a line.

Value: $16$ 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: $16$ Checked construction
no-three-in-line-8-lower-16, 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: $16$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
1906-11-07 Lower bound: $16$
H.E. Dudeney, The Tribune, November 7, 1906. Reprinted as puzzle 317, A puzzle with pawns, in Amusements in Mathematics, Nelson, Edinburgh (1917) 94, 222.
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]