Cage order $n(18,11)$

The order of a $(18,11)$-cage, a $18$-regular graph of girth $11$ with the fewest possible vertices.

Lower bound: $1597339$ (1,597,339) 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: $1597339$ (1,597,339) Lean proof
cage-18-11-lower-1597339, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

No updates recorded.