On Orthogonal Arrays

Abstract

It was shown in [11] that one can construct orthogonal arrays $(\lambda 2^3, k + 1, 2, 3)$ from arrays $(\lambda 2^2, k, 2, 2)$ with the maximum number of constraints $k + 1$ provided that $k$ is the maximum number of constraints for the arrays of strength two. This result is generalized here to construction of arrays $(\lambda 2^{t + 1}, k + 1, 2, t + 1)$ from arrays $(\lambda 2^t, k, 2, t)$. The structure of arrays $(\lambda 2^t, t + 1, 2, t)$ is analyzed and for $\lambda = q2^n, q$ odd, a method of extending any array $(\lambda 2^t, t + 1, 2, t)$ to $t + n + 1$ constraints is described. Orthogonal arrays $(\lambda 2^4, k, 2, 4)$ are discussed in detail for $\lambda = 1$ through $\lambda = 5$. The maximum value of $k$ is established in each of these cases and arrays assuming these values are effectively constructed.