On the Structure of Small Strength-2 Covering Arrays
Résumé
A covering array CA(N ; t, k, v) of strength t is an N × k array of symbols from an alphabet of size v such that in every N × t subarray, every t-tuple occurs in at least one row. A covering array is optimal if it has the smallest possible N for given t, k, and v, and uniform if every symbol occurs N/v or N/v times in every column. Prior to this paper the only known optimal covering arrays for t = 2 were orthogonal arrays, covering arrays with v = 2 constructed from Sperner's Theorem and the Erdős-Ko-Rado Theorem, and eleven other parameter sets with v > 2 and N > v 2. In all these cases, there is a uniform covering array with the optimal size. It has been conjectured that there exists a uniform covering array of optimal size for all parameters. In this paper a new lower bound as well as structural constraints for small uniform strength-2 covering arrays are given. Moreover, covering arrays with small parameters are studied computationally. The size of an optimal strength-2 covering array with v > 2 and N > v 2 is now known for 21 parameter sets. Our constructive results continue to support the conjecture.
Domaines
Mathématique discrète [cs.DM]Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...