## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

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