On some parametric classifications of quasi-symmetric 2-designs

Abstract

Abstract. Quasi-symmetric 2-designs with block intersection numbers x and y, where y = x + 4 and x > 0 are considered. If D(v, b, r, k, λ; x, y) is a quasi-symmetric 2-design with above condition, then it is shown that the number of such designs is finite, whenever 3 ≤ x ≤ 68. Moreover, the non-existence of triangle free quasi-symmetric 2-designs under these parameters is obtained.