Indecomposable Simple $2-(v,\mathrm{\&},4)$ Designs of Small Orders

Abstract

In this paper, simple $2-(9,4,\lambda )$ designs are constructed for $\lambda =3q$, $1\le q\le 7$, and indecomposable simple $2-(v,k,\lambda )$ designs are constructed for all $10\le v\le 16$ and the smallest possible $\lambda$ for which the existence of simple $2-(v,k,\lambda )$ designs was previously undecided.