Cage order $n(3,15)$
The order of a $(3,15)$-cage, a $3$-regular graph of girth $15$ with the fewest possible vertices.
Lower bound:
$384$
Upper bound:
$620$
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:
$382$
Lean proof
cage-3-15-lower-382, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
-
Upper bound: $620$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $384$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]