Simple t-designs: A recursive construction for arbitrary t

TL;DR

This paper introduces a recursive combinatorial method for constructing simple t-designs for any t, enabling the discovery of many previously unknown designs.

Contribution

It presents a new recursive construction technique for simple t-designs applicable to any t, expanding the catalog of known designs.

Findings

Found numerous new t-designs using the recursive method

Demonstrated the method's usefulness and power through examples

Provided a set of solutions satisfying the required equalities

Abstract

The aim of this paper is to present a recursive construction of simple t-designs for arbitrary t. The construction is of purely combinatorial nature and it requires finding solutions for the indices of the ingredient designs that satisfy a certain set of equalities. We give a small number of examples to illustrate the construction, whereby we have found a large number of new t-designs, which were previously unknown. This indicates that the method is useful and powerful.