The Coexistence of Some Binary and $N$-Ary Designs

Abstract

It is shown that the existence of a semi-regular automorphism group of order $m$ of a binary design with $v$ points implies the existence of an $n$-ary design with $v/m$ points. Several examples are described. Examples of other $n$-ary designs are considered which place such $n$-ary designs in context among $n$-ary designs generally.