Quasi-symmetric balanced incomplete block designs

AbstractA balanced incomplete block design (v, b, r, k, λ) is called quasi-symmetric if each block intersects one other block in x varieties and the remaining b−2 blocks in y varieties each. We show that there are only two families of such designs:(a) designs formed by two copies of (v, v, k, k, λ);(b) designs with parameters (4y, 8y−2, 4y−1, 2y, 2y−1).A more general problem is suggested