## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 23, Number 3 (1952), 426-434.

### Orthogonal Arrays of Index Unity

#### Abstract

In this paper we shall proceed to generalize the notion of a set of orthogonal Latin squares, and we term this extension an orthogonal array of index unity. In Section 2 we secure bounds for the number of constraints which are the counterpart of the familiar theorem which states that the number of mutually orthogonal Latin squares of side $s$ is bounded above by $s - 1$. Curiously, our bound depends upon whether $s$ is odd or even. In Section 3 we give a method of constructing these arrays by considering a class of polynomials with coefficients in the finite Galois field $GF(s)$, where $s$ is a prime or a power of a prime. In the concluding section we give a brief discussion of designs based on these arrays.

#### Article information

**Source**

Ann. Math. Statist., Volume 23, Number 3 (1952), 426-434.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177729387

**Digital Object Identifier**

doi:10.1214/aoms/1177729387

**Mathematical Reviews number (MathSciNet)**

MR49146

**Zentralblatt MATH identifier**

0047.01704

**JSTOR**

links.jstor.org

#### Citation

Bush, K. A. Orthogonal Arrays of Index Unity. Ann. Math. Statist. 23 (1952), no. 3, 426--434. doi:10.1214/aoms/1177729387. https://projecteuclid.org/euclid.aoms/1177729387