There exists a (99,14,1,2)-strongly regular graph? That is a graph with 99 vertices, each vertex connected with 14 other vertices, each edge entering in a unique triangle, and such that for each non-connected pair of vertices $a$, $b$, there exist other two $c$ and $d$, and only those two, connected simultaneously with $a$ and $b$?

All the restrictions studied do not rule out the existence, but nobody has been able to construct it. E. Berlekamp, J. H. van Lint y J. J. Seidel have constructed a (243,22,1,2)-strongly regular graph. (A strong Regular Graph Derived from the Perfect Ternary Golay Code, in the book A Survey of Cominatorial Theory, ed. by J. N. Srivastava, North Holland, 1973, p.~25–30.)