Degree-diameter problem $N(4,6)$

The largest possible number of vertices in a graph of maximum degree $4$ and diameter $6$.

Updates

• 1994-11-03 Lower bound: $740$
  Comellas, F., & Gómez, J. (1994). New large graphs with given degree and diameter. arXiv preprint math/9411218.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]