Optimum super-simple mixed covering arrays of type a 1 b k−1

Abstract

A mixed covering array (MCA) of type (v1, v2,..., vk), denoted by MCAλ (N; t, k, (v1, v2,..., vk)), is an N × k array with entries in the i-th column from a set Vi of vi symbols and has the property that each N × t sub-array covers all the t-tuples at least λ times, where 1 ≤ i ≤ k. An MCAλ(N; t, k, (v1, v2,..., vk)) is said to be super-simple, if each of its N × (t + 1) sub-arrays contains each (t + 1)-tuple at most once. Recently, it was proved by Tang, Yin and the author that an optimum super-simple MCA of type (a, b, b,..., b) is equivalent to a mixed detecting array (DTA) of type (a, b, b,..., b) with optimum size. Such DTAs can be used to generate test suites to identify and determine the interaction faults between the factors in a component-based system. In this paper, some combinatorial constructions of optimum super-simple MCAs of type (a, b, b,..., b) are provided. By employing these constructions, some optimum super-simple MCAs are then obtained. In particular, the spectrum across which optimum super-simple MCA2(2b2; 2, 4, (a, b, b, b))′s exist, is completely determined, where 2 ≤ a ≤ b.