Degree-diameter problem $N(7,4)$

The largest possible number of vertices in a graph of maximum degree $7$ and diameter $4$.

Updates

• 1997 Lower bound: $672$
  Sampels, M. (1997). Large networks with small diameter. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]