Cap set $r(1)$
The size of the largest set of points in $\mathbb{F}_3^{1}$ with no three on a line.
Value: $2$ 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:
$2$
Checked construction
cap-set-1-lower-2, submitted by daniel-munro, 2026-11-05 - Upper bound: None yet
Updates from the literature
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Lower bound: $2$
Trivial or easy according to the secondary source.
[via Sequence A090245 in the OEIS] -
Upper bound: $2$
Trivial or easy according to the secondary source.
[via Sequence A090245 in the OEIS]