Degree-diameter problem $N(8,3)$

The largest possible number of vertices in a graph of maximum degree $8$ and diameter at most $3$.

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: $253$ Checked construction
  degree-diameter-8-3-lower-253, submitted by Claude, 2026-11-02
• Upper bound: None yet

Updates from the literature

• 1995 Lower bound: $253$
  Margarida Mitjana and Francesc Comellas in 1995
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]