Cage order $n(19,15)$

The order of a $(19,15)$-cage, a $19$-regular graph of girth $15$ with the fewest possible vertices.

Lower bound: $684245918$ (684,245,918) 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: $684245918$ (684,245,918) Lean proof
cage-19-15-lower-684245918, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

No updates recorded.