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December, 1961 On Some Methods of Construction of Partially Balanced Arrays
I. M. Chakravarti
Ann. Math. Statist. 32(4): 1181-1185 (December, 1961). DOI: 10.1214/aoms/1177704857


Partially balanced arrays are generalizations of orthogonal arrays. Multifactorial designs derived from partially balanced arrays require a reduced number of assemblies in order to accommodate a given number of factors. For instance, an orthogonal array of strength two, six symbols and four constraints, would require at least $2.6^2 = 72$ assemblies. This is because there does not exist a pair of mutually orthogonal Latin Squares of order six. But for the same situation, a partially balanced array in 42 assemblies, is constructed in this paper. The method of construction is one of composition which utilizes the existence of a pairwise partially balanced incomplete block design and an orthogonal array.


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I. M. Chakravarti. "On Some Methods of Construction of Partially Balanced Arrays." Ann. Math. Statist. 32 (4) 1181 - 1185, December, 1961.


Published: December, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0107.36002
MathSciNet: MR130770
Digital Object Identifier: 10.1214/aoms/1177704857

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 4 • December, 1961
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