No-three-in-line $D(53)$

106 points of the 53 by 53 grid with no three on a line

The largest number of points of the $53 \times 53$ grid with no three on a line.

Value: $106$ 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: $106$ Checked construction
no-three-in-line-53-lower-106, submitted by daniel-munro, 2026-11-05
[construction from T. Prellberg, No three in line configurations, OEIS A272651 (2026-02-20).]
Upper bound: None yet

Updates from the literature

Upper bound: $106$
Trivial or easy according to the secondary source.
[via No-three-in-line problem - Wikipedia]
2025-10-28 Lower bound: $106$
T. Prellberg, personal communication, recorded on the no-three-in-line records page (2025-10-28).
[via The No-Three-in-Line Problem, Achim Flammenkamp, 2026-10-28]