Covering and radius-covering arrays: Constructions and classification

The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays, explicit constructions from covering codes are developed. Lower bounds are improved upon using connections to orthogonal arrays, partition matrices, and covering codes, and in specific cases by computation. Consequently for some parameter sets the minimum size of a covering array is determined precisely. For certain of these, a complete classification of all inequivalent covering arrays is determined, again using computational techniques. Existence tables for up ∗Corresponding author Email addresses: [email protected] (C. J. Colbourn), [email protected] (G. Kéri ), [email protected] (P. P. Rivas Soriano ), [email protected] (J.-C. Schlage-Puchta ) Preprint submitted to Elsevier November 20, 2009 to 10 columns, up to 8 symbols, and all possible strengths are presented to report the best current lower and upper bounds, and classifications of inequivalent arrays.