A new upper bound on the parameters of quasi-symmetric designs

On some parametric classifications of quasi-symmetric 2-designs

“…Let D be a quasi-symmetric 2-design with standard parameter set (2,18,2496), (3,7,1456), (3,11,3200), (4,12,3840), (4,19,2964), (5,13,4544), (6,14,5312), (7,15,6144), (9,24,2841). But for these values of x, k and M , we are not getting any positive integral solutions of λ from the quadratic equation Aλ 2 + B λ + C = 0 and hence no triangle free quasi-symmetric 2-designs can exist under these parametrical restrictions.…”

“…During the last several decades quasi-symmetric 2-designs and their classification play an important role to the study of design theory see for example [6,10,12,13,15,16,18]. Many results have been developed in the theory of binary codes, basically on self-complementary codes, self-dual codes using such designs.…”