Distance-regular graph with intersection array {140,108,18;1,18,105} does not exist

Distance-regular graph Γ of diameter 3 having the second eigenvalue θ1=a3 is called Shilla graph. In this case a=a3 devides k and we set b=b(Γ)=k/a. Jurishich and Vidali found intersection arrays of Q-polynomial Shilla graphs with b2=c2: {2rt(2r+1),(2r-1)(2rt+t+1),r(r+t);1,r(r+t),t(4r2-1)}. But many arrays in this series are not feasible. Belousov I. N. and Makhnev A. A. found a new infinite series feasible arrays of Q-polynomial Shilla graphs with b2=c2 (t=2r2-1): {2r(2r2-1)(2r+1),(2r-1)(2r(2r2-1)+2r2),r(2r2+r-1);1,r(2r2+r-1),(2r2-1)(4r2-1)}. If r=2 then we have intersection array {140,108,18;1,18,105}. In the paper it is proved that graph with this intersection array does not exist.