ABSTRACT

A geometric structure can be studied by using a representation of this in another one. A very nice application of this fact is given by the representation of translation planes (in particular the non-Desarguesian ones) in high dimensional (Desarguesian) projective spaces. The above constructions allow also generalizations which lead to classes of incidence structures different from planes. Well known examples were given by Heft who constructed various classes of divisible designs and partial designs. Various other ways based on properties of finite geometric structures are leading to the construction of classes of designs. Some of these may be based on the existence of a covering or of a partition of a geometric object obtained using substructures of some type.