A practical method is described for deciding whether or not a nite-dimensional module for a group over a nite eld is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalisation of the Parker-Norton`Meataxe' algorithm, but it does not depend for its eeciency on the eld being small. The principal tools involved are the calculation of the nullspace and t...

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.