Further results on nearly Kirkman triple systems with subsystems
type: Item
instance of: scholarly article
title: Further results on nearly Kirkman triple systems with subsystems
zbMATH Open document ID: 1029.05019
DOI: 10.1016/S0012-365X(02)00749-5
author: Dameng Deng
author: Hao Shen
author: R. S. Rees
published in: Discrete Mathematics
publication date: 2003-09-04T00:00:00Z
review text: The known existence results for nearly Kirkman triple systems (NKTSs) with subsystems are improved upon. For an NKTS of order \(u\) to have an NKTS of order \(v\) as a subsystem, basic necessary conditions are that \(v\equiv u\equiv 0\pmod 6\), \(u\geq 3v\) and \(v\geq 18\). These conditions are shown to be sufficient whenever \(18\leq v\leq 72\), and also when \(u\geq 3.5v\) and \(v\geq 78\). Many new NKTSs with subsystems, and some new 4-GDDs, found by computer-assisted direct construction, are also presented.
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 1974986
zbMATH Keywords: nearly resolvable design
reviewed by: Charles J. Colbourn
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00749-5
OpenAlex ID: W2078953187
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description: scientific article; zbMATH DE number 1974986