Group divisible designs with block size four and group type \(g^um^1\)
type: Item
instance of: scholarly article
title: Group divisible designs with block size four and group type \(g^um^1\)
zbMATH Open document ID: 1307.05025
author: Hengjia Wei
author: Gennian Ge
published in: Designs, Codes and Cryptography
publication date: 2015-01-23T00:00:00Z
review text: In this paper the authors consider the existence problem for \(\{4\}\)-GDDs of type \(g^{u}m^{1}\) and show that the necessary conditions for the existence of such a GDD with \(g,m>0\) and \(u\geq 4\), are also sufficient except for \((g,m,u)=(2,6,5)\) and except possibly for some cases listed in the paper. Some possible exceptions can be removed from the list by constructing \(\{4\}\)-GDDs of type \(2^{39}35^{1}\), \(6^{13}27^{1}\) and \(6^{13}33^{1}\) or of type \(g^{6}m^{1}\) with \(g\equiv 2,4 \pmod 6\).
reviewed by: Ioan Tomescu
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 6390340
zbMATH Keywords: group divisible design
zbMATH Keywords: double group divisible design
zbMATH Keywords: incomplete group divisible design
zbMATH Keywords: non-uniform group divisible design
MaRDI profile type: Publication
full work available at URL: s10623-013-9854-z
OpenAlex ID: W2081639058
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DOI: 10.1007/S10623-013-9854-Z
description: scientific article; zbMATH DE number 6390340