Cage order $n(8,12)$
The order of a $(8,12)$-cage, a $8$-regular graph of girth $12$ with the fewest possible vertices.
Value: $39216$ (39,216) 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:
$39216$
(39,216)
Lean proof
cage-8-12-lower-39216, submitted by Claude, 2026-10-29 - Upper bound: None yet
Updates from the literature
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Upper bound: $39216$
(39,216)
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]