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New covering array numbers

Author

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  • Izquierdo-Marquez, Idelfonso
  • Torres-Jimenez, Jose

Abstract

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.

Suggested Citation

  • Izquierdo-Marquez, Idelfonso & Torres-Jimenez, Jose, 2019. "New covering array numbers," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 134-146.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:134-146
    DOI: 10.1016/j.amc.2019.01.069
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    Cited by:

    1. Torres-Jimenez, Jose & Acevedo-Juárez, Brenda & Avila-George, Himer, 2021. "Covering array EXtender," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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