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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.
|Number of pages||20|
|Journal||Journal of Combinatorial Designs|
|Early online date||1 Jan 2019|
|Publication status||Published - Jan 2020|
|MoE publication type||A1 Journal article-refereed|
- computational enumeration
- covering array
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Classification of small strength-2 covering arrays
Kokkala, J. (Creator), Meagher, K. (Creator), Reza, N. (Creator), Nurmela, K. (Creator), Östergård, P. (Creator) & Stevens, B. (Creator), 31 Oct 2018
- 1 Finished
Construction and Classification of Discrete Mathematic Structures
Kokkala, J., Laaksonen, A., Östergård, P., Szollosi, F. & Pöllänen, A.
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding