Degree-diameter problem $N(6,3)$

The largest possible number of vertices in a graph of maximum degree $6$ and diameter $3$.

Updates

• 2001-05-25 Lower bound: $110$
  Exoo, G. (2001). A family of graphs and the degree/diameter problem. Journal of Graph Theory, 37(2), 118-124.
• 2001-06 Lower bound: $111$
  Geoffrey Exoo, after May 2001 (i.e. after https://doi.org/10.1002/jgt.1007)
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]