Degree-diameter problem $N(12,4)$

The largest possible number of vertices in a graph of maximum degree $12$ and diameter $4$.

Lower bound: $4680$
Upper bound: Unknown

Updates

1982 Lower bound: $4680$
Bermond, J. C., Delorme, C., & Farhi, G. (1982). Large graphs with given degree and diameter III. In North-Holland Mathematics Studies (Vol. 62, pp. 23-31). North-Holland.
[via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]