Cage order $n(8,8)$
The order of a $(8,8)$-cage, a $8$-regular graph of girth $8$ with the fewest possible vertices.
Value: $800$ Verified lower bound (not in the literature) Verified upper bound
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:
$800$
Lean proof
cage-8-8-lower-800, submitted by Claude, 2026-10-29 -
Upper bound:
$800$
Checked construction
cage-8-8-upper-800, submitted by Claude, 2026-10-28
Updates from the literature
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Upper bound: $800$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]