Cage order $n(7,8)$
The order of a $(7,8)$-cage, a $7$-regular graph of girth $8$ with the fewest possible vertices.
Lower bound:
$518$
Verified
(not in the literature)
Upper bound:
$672$
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:
$518$
Lean proof
cage-7-8-lower-518, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
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Upper bound: $672$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]