Cage order $n(18,14)$

The order of a $(18,14)$-cage, a $18$-regular graph of girth $14$ with the fewest possible vertices.

Lower bound: $51292334$ (51,292,334) Verified (not in the literature)
Upper bound: Unknown

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: $51292334$ (51,292,334) Lean proof
cage-18-14-lower-51292334, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

No updates recorded.