Construction of non-isomorphic covering arrays

Abstract

A covering array CA([Formula: see text]) of strength [Formula: see text] and order [Formula: see text] is an [Formula: see text] array over [Formula: see text] with the property that every [Formula: see text] subarray covers all members of [Formula: see text] at least once. When the value of [Formula: see text] is the minimum possible it is named as the covering array number (CAN) i.e. [Formula: see text]. Two CAs are isomorphic if one of them can be derived from the other by a combination of a row permutation, a column permutation, and a symbol permutation in a subset of columns. Isomorphic CAs have equivalent coverage properties, and can be considered as the same CA; the truly distinct CAs are those which are non-isomorphic among them. An interesting and hard problem is to construct all the non-isomorphic CAs that exist for a particular combination of the parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We constructed the non-isomorphic CAs for 70 combinations of values of the parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the results allow us to determine CAN(3,13,2) =16, CAN(3,14,2) =16, CAN(3,15,2) =17, CAN(3,16,2) =17, and CAN(2,10,3) =14. The exact lower bound for these covering arrays numbers had not been determined before either by computational search or by algebraic analysis.