Distance-regular graphs with intersection arrays {7,6,6;1,1,2} and {42,30,2;1,10,36} do not exist

Let Γ be a distance-regular graph of diameter 3 without triangles, u be a vertex of the graph~Γ, Δi=Γi(u) and Σi=Δi2,3. Then Σi is a regular graph without 3-cocliques of degree k′=ki-ai-1 on v′=ki vertices. Note that for non-adjacent vertices y,z∈Σi we have Σi={y,z}∪Σi(y)∪Σi(z). Therefore, for μ′=|Σi(y)∩Σi(z)| we have the equality v′=2k′+2-μ′. Hence the graph Σ is coedge regular with parameters (v′,k′,μ′). It is proved in the paper that a distance-regular graph with intersection array {7,6,6;1,1,2} does not exist. In the article by M. S. Nirova "On distance-regular graphs with θ2=-1" is proved that if there is a strongly regular graph with parameters (176,49,12,14), in which the neighborhoods of the vertices are 7×7 -lattices, then there also exists a distance-regular graph with intersection array {7,6,6;1,1,2}. M. P. Golubyatnikov noticed that for a distance-regular graph Γ with intersection array {7,6,6;1,1,2} graph Γ2 is distance regular with intersection array {42,30,2;1,10,36}. With this result and calculations of the triple intersection numbers, it is proved that the distance-regular graphs with intersection arrays {7,6,6;1,1,2} and {42,30,2;1,10,36} do not exist.