The Spectra for the Conjugate Invariant Subgroups of n2 × 4 Orthogonal Arrays

Abstract

An n2 × k orthogonal array is a pair (P, B) where P = {1, 2, …, n} and B is a collection of k-tuples of elements from P (called rows) such that if i < j ∈ {1, 2, …, k} and x and y are any two elements of P (not necessarily distinct) there is exactly one row in B whose ith coordinate is x and whose jth coordinate is y. We will refer to the ith coordinate of a row r as the ith column of r. The number n is called the order (or size) of the array and k is called the strength.