Existence of strongly regular graphs for the remaining lambda-one, mu-two parameter sets

Determine whether strongly regular graphs exist with parameter sets $(99,14,1,2)$, $(6273,112,1,2)$, and $(494019,994,1,2)$, thereby resolving the corresponding unresolved existence questions, including Conway’s 99-graph problem for $(99,14,1,2)$.

Background

The paper identifies five possible parameter sets for strongly regular graphs with $\lambda=1$ and $\mu=2$. Two of these, $(9,4,1,2)$ and $(243,22,1,2)$, are known to exist, while the existence of three others is unresolved. The parameter set $(99,14,1,2)$ is especially prominent as Conway’s 99-graph problem. The paper derives the spectra that the associated 3-clique graphs would have if the unresolved strongly regular graphs existed, but it does not settle their existence.