On quasi-symmetric designs

In this paper we show that Lander's coding-theoretic proof of (parts of) the Bruck-Ryser-Chowla Theorem can be suitably modified to obtain analogous number theoretic restrictions on the parameters of quasi-symmetric designs. These results may be thought of as extensions to odd primes of the recent binary nonexistence results due to Calderbank et al. The results in this paper kill infinitely many feasible parameters for quasi-symmetric designs.