Cage order $n(18,8)$
The order of a $(18,8)$-cage, a $18$-regular graph of girth $8$ with the fewest possible vertices.
Value: $10440$ (10,440) Verified lower bound (not in the literature)
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.
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Lower bound:
$10440$
(10,440)
Lean proof
cage-18-8-lower-10440, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
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Upper bound: $10440$
(10,440)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]