Extended directed triple systems

Let {n;b2,b1}{n;b2,b1} denote the class of extended directed triple systems of the order n   in which the number of blocks of the form [a,b,a][a,b,a] is b2b2 and the number of blocks of the form [b,a,a][b,a,a] or [a,a,b][a,a,b] is b1b1. In this paper, we have shown that the necessary and sufficient condition for the existence of the class {n;b2,b1}{n;b2,b1} is b1≠1b1≠1, 0⩽b2+b1⩽n0⩽b2+b1⩽n and(1)b2≡b1(mod3) for n≢2(mod3);(2)b2≡b1+1(mod3) for n≡2(mod3).