Constructions of doubly resolvable Steiner quadruple systems
type: Item
instance of: scholarly article
title: Constructions of doubly resolvable Steiner quadruple systems
zbMATH Open document ID: 1472.05026
author: Zhaoping Meng
author: Bin Zhang
author: Zhanggui Wu
published in: Designs, Codes and Cryptography
publication date: 2021-05-10T00:00:00Z
review text: A Steiner quadruple system (SQS\((v)\)) is a design with block size 4 in which every set of three points lies in exactly one block. This paper gives two general constructions for doubly resolvable SQS\((v)\)s; one obtains a doubly resolvable SQS\((2v)\) from a doubly resolvable SQS\((v)\), and the other makes use of doubly resolvable candelabra quadruple systems. Using these, doubly resolvable SQS\((v)\)s are obtained for \(m \in \{1,5,7,11,17,26\}\) and \(n\) a positive integer, whenever $v$ is of one of the following forms: $m \cdot 2^n$ with $n \geq 2$, $(m,n) \neq (1,3)$, and $(3m \cdot 2^n) - 16$ with $n \geq 4$, $(m,n) \neq (1,5)$.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 7346955
zbMATH Keywords: Steiner quadruple system
zbMATH Keywords: doubly resolvable
zbMATH Keywords: orthogonal Latin squares
zbMATH Keywords: candelabra quadruple system
reviewed by: R. Julian R. Abel
MaRDI profile type: Publication
full work available at URL: s10623-021-00844-0
OpenAlex ID: W3127319965
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DOI: 10.1007/S10623-021-00844-0
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description: scientific article; zbMATH DE number 7346955