Strongly regular graphs with parameters (85,14,3,2) do not exist

We investigate the second smallest unresolved feasible set of parameters of strongly regular graphs, $(v,k,λ,μ)=(85,14,3,2)$. Using the classification of cubic graphs of small degree, we restrict possible local structure of such a graph G. After that, we exhaustively enumerate possible neighbourhoods of a maximal $3$-clique of G and check them against a variety of conditions, including the combinatorial ones, coming from $λ=3$ and $μ=2$, as well as the linear algebra ones, utilising the Euclidean representation of G. These conditions yield contradiction in all cases, and hence, no srg(85,14,3,2) exists.