On the construction and existence of orthogonal arrays with three levels and indexes 1 and 2
type: Item
instance of: scholarly article
title: On the construction and existence of orthogonal arrays with three levels and indexes 1 and 2
zbMATH Open document ID: 0886.05033
author: J. Ning
published in: The Annals of Statistics
publication date: 1998-04-20T00:00:00Z
review text: An \(N\times k\) matrix \(A\) with entries from a set \(S\) of cardinality \(s\) is called an orthogonal array of strength \(t\), \(1\leq t\leq k\), denoted by \(\text{OA}(N,k,s,t)\), if every \(N\times t\) submatrix of \(A\) contains each \(t\)-tuple based on \(S\) equally often as a row. The common frequency \(\lambda= N/2^t\) with which each of the \(t\)-tuples appears as a row in a submatrix is called the index of the array. The authors provide the construction of orthogonal arrays with three levels and index 2. For strengths greater than or equal to 2, they show that orthogonal arrays with 3 levels and index 1 are unique. Finally they establish that the maximum number of factors is \(k\) for orthogonal arrays with 3 levels and index 2. The paper disappoints and mentions very little, if any, on connections of OA's with codes, linear codes and recent results on these topics (e.g., \textit{B. L. Raktoe} and \textit{H. Pesotan} [Math. Methods Stat. 5, No. 2, 244-252 (1996)] as related to saturated \(s^{k-p}_R\) fractional factorial designs, where \(N= s^q\), \(q=k-p\), and \(R= t+1\), \(s\) is a prime or prime power).
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 62K15
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 1093135
zbMATH Keywords: orthogonal array
zbMATH Keywords: linear codes
zbMATH Keywords: fractional factorial designs
reviewed by: B. Leo Raktoe
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1069362386
OpenAlex ID: W2049629895
DOI: 10.1214/AOS/1069362386
description: scientific article; zbMATH DE number 1093135