Covering arrays with mixed alphabet sizes

Covering arrays with mixed alphabet sizes, or simply mixed covering arrays, are natural generalizations of covering arrays that are motivated by applications in software and network testing. A (mixed) covering array A of type Pi(i=1)(k) g(i) is a k x N array with the cells of row i filled with elements from Z(gi) and having the property that for every two rows i and j and every ordered pair of elements (e, f) is an element of Z(gi) X Z(gj), there exists at least one column c, 1 less than or equal to c less than or equal to N, such that A(i,c) = e and A(j,c) = f. The (mixed) covering array number, denoted by ca(Pi(i=1)(k) g(i)), is the minimum N for which a covering array of type Pi(i=1)(k) g(i) with N columns exists. In this paper, several constructions for mixed covering arrays are presented, and the mixed covering array numbers are determined for nearly all cases with k = 4 and for a number of cases with k = 5. (C) 2003 Wiley Periodicals, Inc.