Group divisible designs with block size five: direct constructions

TL;DR

This paper presents direct construction methods for a large class of group divisible designs with block size five, significantly expanding the known configurations especially of type g^u m^1.

Contribution

It introduces new direct construction techniques for 233 group divisible designs with block size five, mainly of type g^u m^1, enhancing design theory.

Findings

Constructed 233 new group divisible designs with block size five.

Most designs are of type g^u m^1, with m > 0.

Provides explicit methods for direct construction.

Abstract

We give direct constructions for 233 group divisible designs with block size five, mostly of type $g^u m^1$, $m > 0$.