On q-polynomial Shilla graphs with b=6

Distance-regular raph Γ of diameter 3, having the second eigenvalue θ1=a3 is called Shilla graph. For such graph a=a3 devides k and we set b=b(Γ)=k/a. Further a1=a-b and Γ has intersection array {ab,(a+1)(b-1),b2;1,c2,a(b-1)}. I. N. Belousov and A. A. Makhnev found feasible arrays of Q-polynomial Shilla graphs with b=6: {42t,5(7t+1),3(t+3);1,3(t+3),35t}, where t∈{7,12,17,27,57}, {312,265,48;1,24,260}, {372,315,75;1,15,310}, {624,525,80;1,40,520}, {744,625,125;1,25,620}, {930,780,150;1,30,775}, {1794,1500,200;1,100,1495} or {5694,4750,600;1,300,4745}. It is proved in the paper that graphs with intersection arrays {372,315,75;1,15,310}, {744,625,125;1,25,620} and {1794,1500,200;1,100,1495} do not exist.