On the structure of small strength-2 covering arrays

Research output: Contribution to journalArticleScientificpeer-review

Researchers

Research units

  • University of Regina
  • CNRS/IN2P3
  • Carleton University
  • Aalto University

Abstract

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. Before 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 11 other parameter sets with v > 2 and N > v2. 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 is given. Moreover, covering arrays with small parameters are studied computationally. The size of an optimal strength-2 covering array with v > 2 and N > v2 is now known for 21 parameter sets. Our constructive results continue to support the conjecture.

Details

Original languageEnglish
JournalJournal of Combinatorial Designs
Publication statusE-pub ahead of print - 1 Jan 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • bounds, computational enumeration, covering array

ID: 37071622