On a Class of Strongly Regular Designs and Quasi-semisymmetric Designs

摘要

Motivated from a study of dual polar graphs and alternating bilinear form graphs, the notion of quasi-sernisymmetric designs is introduced as a class of strongly regular designs. Some necessary conditions among their parameters are derived in terms of associated incidence graphs and intersection diagrams. Two geometric conditions are introduced, leading to a joint classification of some types of polar spaces and Milne polar spaces, and then their corresponding point graphs as well. Three families of quasi-semisymmetric designs with nexus are constructed in terms of orthogonal arrays, hyper-planes and difference sets, respectively. Moreover, an upper bound for the number of points is also derived.