The Annals of Mathematical Statistics

Orthogonal Arrays of Index Unity

K. A. Bush

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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.

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

First available in Project Euclid: 28 April 2007

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

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