Topological Invariants of 2-Designs Arising from Difference Families

Hefftner, White, Alpert, and others observed a connection between topology and certain block designs with parameters k = 3 and ,I= 2. In this paper the connection is extended to include all values of I.. The topology is also exploited further to produce some new invariants of designs. The topology also gives an upper bound for the order of the automorphism group of the designs studied which leads to a generalization of the Bays-Lambossy theorem. Methods for constructing block designs are also given showing that the results apply and are useful for a large class of designs.