On $t$-designs

Abstract

We present the generalization (conjectured by A. Ja. Petrenjuk) of Fisher's Inequality b>v for 2-designs and Petrenjuk's Inequality ^^(2) f°r 4-designs. The ί-designs satisfying the inequality with equality may be considered as generalizatio ns of the symmetric 2-designs (b=v) and have the property that there are exactly — t possible values for the size of the intersection of two distinct blocks, these values being computable from the parameters. * This research was supported in part by ONR NOOO14-67-A-0232-0016 (OSURF