Only two strongly regular graphs with parameters $\lambda=0$ (triangle-free) and $\mu=2$ (any two non-adjacent vertices have exactly two common neighbors) are known, see the wikipedia page: the Clebsch graph and the Sims-Gewirtz graph.

I am looking for any information about the potential existence of more such graphs. For which values of $n$ and $k$ are they known not to exist?

Only few strongly regular graphs with parameters $\lambda=0$ (triangle-free) and $\mu=2$ (any two non-adjacent vertices have exactly two common neighbors) are known, see the wikipedia page: the 4-cycle, the Clebsch graph and the Sims-Gewirtz graph.

I am looking for any information about the potential existence of more such graphs. For which values of $n$ and $k$ are they known not to exist?