New optimal covering arrays using an orderly algorithm

Abstract

A covering array CA(N; t,k,v) is an N × k array such that every N × t subarray covers at least once each t-tuple from v symbols. For given t, k, and v, the minimum number of rows for which exists a CA is denoted by N = CAN(t,k,v) (CAN stands for Covering Array Number) and the corresponding CA is optimal. Optimal covering arrays have been determined algebraically for a small subset of cases; but another alternative to find CANs is the use of computational search. The present work introduces a new orderly algorithm to construct non-isomorphic covering arrays; this algorithm is an improvement of a previously reported algorithm for the same purpose. The construction of non-isomorphic covering arrays is used to prove the nonexistence of certain covering arrays whose nonexistence implies the optimality of other covering arrays. From the computational results obtained, the following CANs were established: CAN(2,k, 3) = 15 for 11 ≤ k ≤ 20, CAN(2, 7, 4)=21, and CAN(2, 5, 6)=39. In addition, the new result CAN(2, 13, 3)=15, and the already known existence of CA(45; 3, 14, 3), imply CAN(3, 14, 3) = 45.