One of the most central problems of modern combinatorial theory is the determination of those parameter triples (v, k, X) for which there exist (0, k, h)-BIBD’s (balanced incomplete block designs). The methods which have been put forth to construct BIBD’s divide roughly into two classes: direct constructions where a BIBD is obtained from an algebraic structure (often a design is constructed fro...

1. Introduction In this paper we consider some results on the orbits of groups of collineations, or, more generally, on the point and block classes of tactical decompositions, on symmetric balanced incomplete block designs (symmetric BIBD = (v, k, 2)-system=finite 2-plane), and we consider generalizations to (not necessarily symmetric) BIBD and other combinatorial designs. The results are about...