The Coexistence of Some Binary and \(N\)-Ary Designs

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.