Open Access
September, 1952 Orthogonal Arrays of Index Unity
K. A. Bush
Ann. Math. Statist. 23(3): 426-434 (September, 1952). DOI: 10.1214/aoms/1177729387


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.


Download Citation

K. A. Bush. "Orthogonal Arrays of Index Unity." Ann. Math. Statist. 23 (3) 426 - 434, September, 1952.


Published: September, 1952
First available in Project Euclid: 28 April 2007

zbMATH: 0047.01704
MathSciNet: MR49146
Digital Object Identifier: 10.1214/aoms/1177729387

Rights: Copyright © 1952 Institute of Mathematical Statistics

Vol.23 • No. 3 • September, 1952
Back to Top