Group divisible designs with block size five

TL;DR

This paper presents new group divisible designs with block size five, expanding the known spectrum of 5-GDDs for specific types, which advances combinatorial design theory.

Contribution

It introduces new group divisible designs with block size five, including types 6^{15} and 10^{15}, extending existing classifications.

Findings

New GDDs of types 6^{15} and 10^{15} identified.

Extended the spectrum for 5-GDDs of type g^u.

Enhanced understanding of combinatorial design structures.

Abstract

We report some group divisible designs with block size five, including types $6^{15}$ and $10^{15}$. As a consequence we are able to extend the known spectrum for 5-GDDs of type $g^u$.