The Solution of the Waterloo Problem

The investigation of symmetric designs is of central interest in design theory. Another class of important incidence structures are projective and affine geometries. A projective geometry gives rise to two symmetric designs, namely the point-hyperplane designs and their complements. It is a remarkable property of these classical symmetric designs that we will investigate in this paper. For the geometric background that is necessary throughout our investigation, we refer the reader to [ 11 ].