On t-Covering Arrays

This paper concerns construction methods for t-covering arrays. Firstly, a construction method using perfect hash families is discussed by combining with recursion techniques and error-correcting codes. In particular, by using algebraic-geometric codes for this method we obtain infinite families of t-covering arrays which are proved to be better than currently known probabilistic bounds for covering arrays. Secondly, inspired from a result of Roux 16] and also from a recent result of Chateauneuf and Kreher 6] for 3-covering arrays, we present several explicit constructions for t-covering arrays, which can be viewed as generalizations of their results for t-covering arrays.