Construction of 3-Designs Using (1,\sigma)-Resolution

Abstract

The paper deals with recursive constructions for simple 3-designs based on other 3-designs having $(1, \sigma)$-resolution. The concept of $(1, \sigma)$-resolution may be viewed as a generalization of the parallelism for designs. We show the constructions and their applications to produce many previously unknown infinite families of simple 3-designs. We also include a discussion of $(1,\sigma)$-resolvability of the constructed designs.