A new look at an old construction: Constructing (simple) 3-designs from resolvable 2-designs

Shrikhande and Raghavarao (1963) published a recursive construction for designs that starts with a resolvable design (the “master design”) and then uses a second design (“the indexing design”) to take certain unions of blocks in each parallel class of the master design. Several variations of this construction have been studied by different authors. We revisit this construction, concentrating on the case where the master design is a resolvable BIBD and the indexing design is a 3-design. We show that this construction yields a 3-design under certain circumstances. The resulting 3-designs have block size k=v/2k=v/2 and they are resolvable. We also construct some previously unknown simple designs by this method.