Cyclic difference packing and covering arrays
Let n and k be positive integers. Let C-q be a cyclic group of order q. A cyclic difference packing (covering) array, or a CDPA(k, n; q) (CDCA(k, n; q)), is a k x n array (a(ij)) with entries a(ij) (0  = 3 exists, and n >= q + 1 if a CDCA(k, n; q) with k = 3 exists. It is proved that a CDCA( 4, q + 1; q) exists for any even positive integers, and so does a CDPA( 4, q - 1; q) or a CDPA( 4, q - 2; q). The result is established, for the most part, by means of a result on cyclic difference matrices with one hole, which is of interest in its own right.
cyclic difference packing/covering array construction