$t$-Covering Arrays Generated by a Tiling Probability Model

A t − α covering array is an m × n matrix, with entries from an alphabet of size α, such that for any choice of t rows, and any ordered string of t letters of the alphabet, there exists a column such that the “values” of the rows in that column match those of the string of letters. We use the Lovász Local Lemma in conjunction with a new tiling-based probability model to improve the upper bound on the smallest number of columns N = N(m, t, α) of a t−α covering array.