Degree-diameter problem $N(12,3)$

The largest possible number of vertices in a graph of maximum degree $12$ and diameter $3$.

Updates

• 2008-06-03 Lower bound: $786$
  Gómez, J. (2009), Some new large (Δ, 3)-graphs. Networks, 53: 1-5.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]