## The Annals of Mathematical Statistics

### On Some Methods of Construction of Partially Balanced Arrays

I. M. Chakravarti

#### Abstract

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

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

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704857

Digital Object Identifier
doi:10.1214/aoms/1177704857

Mathematical Reviews number (MathSciNet)
MR130770

Zentralblatt MATH identifier
0107.36002

JSTOR