Block Designs with SDP Parameters

Abstract

It is traditional to call a quasi-symmetric design with certain parameters an SDP design if the symmetric difference of two different blocks is either a block or a block complement. In this note, we delete the requirements on the parameters and demand just that the symmetric difference of two blocks be a block, a block complement, or either the empty set or the whole point set. We obtain the parameters of such designs and use the result to prove Kantor's theorem on the parameters of a symmetric SDP design. A spin-off of an exponential Diophantine equation considered by Ramanujan is at the core.