Uniformly resolvable three-wise balanced designs with block sizes four and six
type: Item
instance of: scholarly article
title: Uniformly resolvable three-wise balanced designs with block sizes four and six
zbMATH Open document ID: 1191.05021
author: Zhaoping Meng
author: Lijun Ji
author: Beiliang Du
published in: Discrete Mathematics
publication date: 2009-12-15T00:00:00Z
review text: A \(\text{URS}(3,\{4, 6\},v)\) consists of a \(v\)-set and a collection of blocks of size \(4\) or \(6\) such that each \(3\)-subset is contained in a unique block, with the further properties that the set of blocks can be partitioned into parts (called resolution classes) each of which partitions the point set, and that all blocks in a given resolution class are of the same size and so the design is uniform. The authors establish that a \(\text{URS}(3,\{4,6\},v)\) exists if and only if \(v\) is divisible by \(4\). These designs are then used to construct resolvable maximal packings and minimal coverings of triples by quadruples for \(v\) a multiple of \(24\). Results concerning augmented resolvable, and \((1,2)\)-resolvable, Steiner quadruple systems are also obtained.
reviewed by: Chester J. Salwach
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 5648207
zbMATH Keywords: three-wise balanced design
zbMATH Keywords: uniform
zbMATH Keywords: resolvable
zbMATH Keywords: Steiner quadruple system
zbMATH Keywords: packing
zbMATH Keywords: covering
MaRDI profile type: Publication
full work available at URL: j.disc.2009.06.015
OpenAlex ID: W2064259165
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DOI: 10.1016/J.DISC.2009.06.015
description: scientific article; zbMATH DE number 5648207