Quasimultiples of geometric designs

Abstract

We construct quasimultiples of affine planes, inversive planes, and unitals from geometrical configurations in various finite geometries. All designs have k= λ. These designs are simple (no repeated blocks), and all appear to be irreducible in the sense that a quasimultiple of type P will have no subdesign isomorphic to P . This is verified for small orders by computer computations.