The Annals of Mathematical Statistics

On Some Methods of Construction of Partially Balanced Arrays

I. M. Chakravarti

Full-text: Open access


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.

Article information

Ann. Math. Statist., Volume 32, Number 4 (1961), 1181-1185.

First available in Project Euclid: 27 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Chakravarti, I. M. On Some Methods of Construction of Partially Balanced Arrays. Ann. Math. Statist. 32 (1961), no. 4, 1181--1185. doi:10.1214/aoms/1177704857.

Export citation