Balanced ternary designs with block size three, any \(\Lambda\) and any R
type: Item
instance of: scholarly article
title: Balanced ternary designs with block size three, any \(\Lambda\) and any R
zbMATH Open document ID: 0629.05014
DOI: 10.1007/BF02189832
author: Elizabeth J. Billington
published in: Aequationes Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137098
review text: A balanced ternary design with V elements is a collection of B blocks (which are multisets) of size K such that each element occurs 0, 1 or 2 times per block and R times altogether, and such that each unordered pair of distinct elements occur \(\Lambda\) times. Then each element has to occur singly in a constant number \(\rho_ 1\) o blocks and so each element also occurs twice in a constant number \(\rho_ 2\) of blocks, where \(R=\rho_ 1+2\rho_ 2\). If \(\rho_ 2=0\), the design is a balanced incomplete block design (binary design). For non-degeneracy, it is assumed that \(\rho_ 2>0\) and \(K<2V\). Necessarily, \(\Lambda >1\) if \(\rho_ 2>0\) (and \(K>2).\) In this paper, the author gives necessary and sufficient conditions for the existence of a balanced ternary design with \(K=3\), and \(\Lambda >1\) and any \(\rho_ 2>0\).
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 62K10
zbMATH DE Number: 4023295
zbMATH Keywords: balanced ternary design
reviewed by: I. M. Chakravarti
MaRDI profile type: Publication
cites work: More balanced ternary designs with block size three
cites work: Q3968946
cites work: Q3322109
cites work: Graph factorization, general triple systems, and cyclic triple systems
cites work: Q3966159
cites work: Q5813578
OpenAlex ID: W2014355672
description: scientific article; zbMATH DE number 4023295