Towards a Sum-of-Squares Proof for the Nonexistence of Conway's 99-graph

Conway's $99$-graph is a strongly regular graph with parameters $(v,k,λ,μ) = (99,14,1,2)$ and whose existence has long been an open problem. We use both a sum-of-squares program and the fact that a strongly regular graph with $λ= 1, μ= 2$ has no diamond or $K_{2,3}$ subgraph to derive a loose upper