Cage order $n(16,12)$
The order of a $(16,12)$-cage, a $16$-regular graph of girth $12$ with the fewest possible vertices.
Lower bound:
$1627232$
(1,627,232)
Verified
(not in the literature)
Upper bound:
$2088960$
(2,088,960)
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:
$1627232$
(1,627,232)
Lean proof
cage-16-12-lower-1627232, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
-
Upper bound: $2088960$
(2,088,960)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]