Covering arrays, augmentation, and quilting arrays

Abstract

Numerous constructions of the best known covering arrays are effective only for specific numbers of symbols. Fusion replaces numerous symbols by one, and can thereby employ such constructions to produce useful covering arrays on fewer symbols. Augmentation instead replaces one symbol by many, permitting the construction of covering arrays from those with fewer symbols. Until this time, augmentation has been of limited value because it introduces substantial redundant coverage. Here a general augmentation method is improved upon by analyzing the classes of interactions to be covered and employing variants of covering arrays, quilting arrays, to reduce the redundancy introduced. For strengths four, five, and six, quilting arrays are produced that can be used in the refined augmentation to produce many best known covering arrays.