Some New Steiner $2$-Designs $S(2,4,37)$

Abstract

Automorphisms of Steiner $2$-designs $S(2,4,37)$ are studied and used to find many new examples. Some of the constructed designs have $S(2,3,9)$ subdesigns, closing the last gap in the embedding spectrum of $S(2,3,9)$ designs into $S(2,4,v)$ designs.