Degree-diameter problem $N(4,3)$

The largest possible number of vertices in a graph of maximum degree $4$ and diameter $3$.

Updates

• 1992-07-15 Lower bound: $41$
  Allwright, J. (1992). New (Δ, D) graphs discovered by heuristic search. Discrete Applied Mathematics, 37, 3-8.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]