Detecting arrays and their optimality

Detecting arrays were proposed by Colbourn and McClary in 2008, which are of interest in generating software test suites to cover all t-sets of component interactions and detect interaction faults in component-based systems. So far, optimality and constructions of detecting arrays have not been studied systematically. Indeed, no useful benchmark to measure the optimality of detecting arrays has previously been given, and only some sporadic examples of optimal detecting arrays have been found. This paper tries to take the first step by presenting a lower bound on the size of detecting arrays and some methods of constructing optimal detecting arrays. A number of infinite series of optimal detecting arrays are then obtained.