Quasi-symmetric designs with the difference of block intersection numbers two

Quasi-symmetric designs with intersection numbers x > 0 and y = x + 2 under the condition λ > 1 are investigated. If D(v, b, r, k, λ; x, y) is a quasi-symmetric design with above conditions then it is shown that either λ = x + 1 or x + 2 or D is a design with the parameters given in the Table 6 or complement of one of these designs.