A recursive construction for simple $t$-designs using resolution

TL;DR

This paper introduces a recursive method to construct simple t-designs by leveraging resolutions of ingredient designs, expanding the possibilities for creating new combinatorial structures.

Contribution

It extends previous construction techniques by incorporating resolution-based mappings, enabling the generation of many new simple t-designs.

Findings

Successfully constructed new simple t-designs

Extended existing design construction methods

Demonstrated applications of the new recursive approach

Abstract

This work presents a recursive construction for simple $t$-designs using resolutions of the ingredient designs. The result extends a construction of $t$-designs in our recent paper [39]. Essentially, the method in [39] describes the blocks of a constructed design as a collection of block unions from a number of appropriate pairs of disjoint ingredient designs. Now, if some pairs of these ingredient $t$-designs have both a suitable $s$-resolution, then we can define a distance mapping on their resolution classes. Using this mapping enables us to have more possibilities for forming blocks from those pairs. The method makes it possible for constructing many new simple $t$-designs. We give some application results of the new construction.