Recursive constructions for 3-designs and resolvable 3-designs

Abstract

Abstract Inspired by the doubling construction method for Steiner quadruple systems and also by a construction of Driessen for 3-designs, we present several recursive constructions for 3-designs and resolvable 3-designs. The construction methods assume the existence of resolvable 3-designs and certain appropriate other 3-designs. They prove to be very useful, as we can construct a large number of new infinite families of 3-designs. Among others we prove, for instance, that for any integer n⩾3, there is a family F n of resolvable 3-designs having parameters 3- (2 j .3.2 n ,2 n ,(2 n−1 −1)(2 n −1) ∏ i=2 n−1 (2 j−i .3.2 n −1)) , for all j⩾0. A list of parameters for newly constructed 3-designs is included.