Quasi-symmetric 3-designs with triangle-free graph

The following result is proved: Let D be a quasi-symmetric 3-design with intersection numbers x, y(0x<y<k). D has no three distinct blocks such that any two of them intersect in x points if and only if D is a Hadamard 3-design, or D has a parameter set (v, k, ) where v=(+2)(²+4+2)+1, k=²+3+2 and =1,2,..., or D is a complement of one of these designs.