Modified group divisible designs with block size 5 and even index
type: Item
instance of: scholarly article
title: Modified group divisible designs with block size 5 and even index
zbMATH Open document ID: 1162.05006
author: R. Julian R. Abel
author: Ahmed M. Assaf
published in: Discrete Mathematics
publication date: 2008-07-11T00:00:00Z
review text: The existence of \((5,\lambda)\)-modified group-divisible designs (MGDDs) is studied when \(\lambda\) is even. The necessary conditions for a \((5,\lambda)\)-MGDD of type \(m^n\) to exist (i.e. \(m \geq 5\); \(n \geq 5\); \(\lambda(nm+1-m-n) \equiv 0 \pmod{4}\); and \(\lambda n m (nm+1-n-m) \equiv 0 \pmod{20}\)) are shown to be sufficient when \(\lambda \geq 4\) is even. When \(\lambda = 2\), sufficiency is established with 13 possible exceptions.
reviewed by: Charles J. Colbourn
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 5300620
zbMATH Keywords: modified group-divisible design
zbMATH Keywords: MGDD
zbMATH Keywords: group-divisible design
zbMATH Keywords: pairwise balanced design
MaRDI profile type: Publication
full work available at URL: j.disc.2007.06.039
OpenAlex ID: W1971136184
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DOI: 10.1016/J.DISC.2007.06.039
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description: scientific article; zbMATH DE number 5300620