The triangle intersection numbers of a pair of disjoint S(2,4,v)S(2,4,v)s

In this paper the triangle intersection problem for a pair of disjoint S(2,4,v)S(2,4,v)s is investigated. Let JT∗(v) denote the set of all integers ss such that there exists a pair of disjoint S(2,4,v)S(2,4,v)s intersecting in ss triangles. Let bv=v(v−1)/12bv=v(v−1)/12. We establish that for any positive integer v≡1,4(mod12), v≥16v≥16 and v≠25,28,37v≠25,28,37, JT∗(v)=[0,bv].