The intersection problem for PBD(4,7*)

For every v equivalent to 7, 10 (mod 12) with v >= 22 there exist a pairwise balanced design PBD of order v with exactly one block of size 7 and rest of size 4, denoted by PBD(4, 7*) of order v. The intersection problem for PBD(4, 7(star)) is the determination of all pairs (v, k) such that there exist a pair of PBD(4, 7(star))s (X, B-1 and (X, B-2) of order v containing the same block B of size 7 such that vertical bar(B-1 \ {B}) boolean AND (B-2 \ {B})vertical bar = k. We will denote the set of all such k by J(v). I(v) {0, 1,..., b(v) - 8, b(v) - 6, b(v)}, where b(v) = (v(2) - v - 42)/12 be the number of blocks of size 4 in PBD(4, 7(star)) of order v. It is established that J(v) = I(v) for any positive integer v equivalent to 7,10 (mod 12) and v is not an element of{10,19,22,31,34, 46, 58, 70}.