A t-\a 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 Lov\'asz 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-\a covering array.Comment: 7 page