New covering array numbers

摘要

A covering array CA(N; t, k, v) is an N × k array on v symbols such that each N × t subarray contains as a row each t-tuple over the v symbols at least once. The minimum N for which a CA(N; t, k, v) exists is called the covering array number of t, k, and v, and it is denoted by CAN(t, k, v). We prove that CA(N;t+1,k+1,v) can be obtained from the juxtaposition of v covering arrays CA(N0; t, k, v), …, CA(Nv−1;t,k,v), where N=∑i=0v−1Ni. Given this, we developed an algorithm that constructs all possible juxtapositions and determines the nonexistence of certain covering arrays which allow us to establish the new covering array numbers CAN(4,13,2)=32, CAN(5,8,2)=52, CAN(5,9,2)=54, CAN(5,14,2)=64, CAN(6, 15, 2) = 128, and CAN(7,16,2)=256. Additionally, the computational results are the improvement of the lower bounds of 13 covering array numbers.