Balanced ternary designs with block size four
type: Item
instance of: scholarly article
title: Balanced ternary designs with block size four
zbMATH Open document ID: 0783.05009
DOI: 10.1016/0378-3758(93)90082-H
author: Elizabeth J. Billington
author: Abdollah Khodkar
author: E. S. Mahmoodian
published in: Journal of Statistical Planning and Inference
publication date: 1993-12-05T00:00:00Z
review text: A \(\text{BTD}(v,\rho_ 2,4,\lambda)\) is a balanced ternary design such that \(k=4\) and each element occurs two times in \(\rho_ 2\) blocks (and, of course, each pair of distinct elements occurs \(\lambda\) times in a block). A necessary existence condition for such a BTD is: if \(\lambda=2\) then \(v \geq 5 \rho_ 2+1\), if \(\lambda=3\) then \(v \geq 4 \rho_ 2 +1\), if \(\lambda \geq 4\) then \(v \geq \lceil 4 \rho_ 2/ \lambda \rceil+1\). The authors show the above conditions are sufficient when \(\rho_ 2 \leq 6\) teaching how to construe such designs by variations of known constructions (mainly Hanani's is used ;see \textit{H. Hanani} [Balanced incomplete block designs and related designs, Discrete Math. 11, 255-369 (1975; Zbl 0361.62067)]). They start from group divisible designs and frame-BTD, previously known or given in a huge table as appendix.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 445193
zbMATH Keywords: balanced ternary design
zbMATH Keywords: frame-BTD
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
cites work: Q3760557
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full work available at URL: 0378-3758(93)90082-h
OpenAlex ID: W2093534132
description: scientific article; zbMATH DE number 445193