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

TL;DR

This paper introduces recursive methods for constructing simple 3-designs using (1, σ)-resolution, generalizing parallelism, leading to new infinite families of such designs and analyzing their resolvability.

Contribution

It presents novel recursive constructions for 3-designs based on (1, σ)-resolution, expanding the known classes of simple 3-designs.

Findings

Produced many new infinite families of simple 3-designs

Demonstrated applications of (1, σ)-resolution in design construction

Discussed the resolvability properties of the constructed designs

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.