Degree-diameter problem $N(19,2)$

The largest possible number of vertices in a graph of maximum degree $19$ and diameter $2$.

Lower bound: $338$
Upper bound: Unknown

Updates

1998-09 Lower bound: $338$
McKay, B. D., Miller, M., & Širáň, J. (1998). A note on large graphs of diameter two and given maximum degree. Journal of Combinatorial Theory, Series B, 74(1), 110-118.
[via The Degree Diameter Problem for General Graphs - Combinatorics Wiki]