On the state of strength‐three covering arrays

By M. Chateauneuf, Donald L. Kreher. 2002

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Group construction of covering arrays (2005, background): “The smallest possible size of a covering array for fixed parameters t; k, and g will be denoted as t-CANðk; gÞ ¼ min l2N fl : there exists a t-CAðl; k; gÞg: For a covering array t-CAðn; k; gÞ, it is clear that n gt, and that t-CANðk; gÞ gt.”
Classification of Orthogonal Arrays by Integer Programming (2008, background): “Chateauneuf and Kreher (2002) provide upper and lower bounds for |CA∗1(k, s, t)| for several k, s combinations and t = 2 or t = 3.”
Covering arrays of higher strength from permutation vectors (2006, background): “The new arrays also provide useful ingredients for ‘‘Roux-type’’ recursive constructions as in [3,4,13].”
Combinatorial aspects of covering arrays (2006, background): “This is smaller than the bound reported by a construction in [20], and matches that found by annealing in [32].”
On optimal superimposed codes (2004, unknown): “We refer to [3] and [32] for tables of g3ðnÞ.”