Cage order $n(16,8)$

The order of a $(16,8)$-cage, a $16$-regular graph of girth $8$ with the fewest possible vertices.

Lower bound: $7232$ Verified (not in the literature)
Upper bound: $8092$

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: $7232$ Lean proof
cage-16-8-lower-7232, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

Upper bound: $8092$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]