DOIAbstract
AbstractA difference covering array with parameters k, n and q, or a DCA(k,n;q) for short, over a group (G,•) of order q is defined to be a k×n array (aij) with entries aij(0⩽i⩽k−1,0⩽j⩽n−1) from G such that, for any two distinct rows t and h(0⩽t<h⩽k−1), every element of G occurs in the difference list {dhj•dtj−1:j=0,1,…,n−1} at least once. It is clear that n⩾q in a DCA(k,n;q). The equality holds if and only if a (q,k,1) difference matrix exists. It is well known that a (q,k,1) difference matrix does not exist, whenever q≡2 (mod4) and k⩾3. Thus, we have n⩾q+1 for these values of k and q. In this article, several constructive techniques for DCAs are presented, and used to solve completely the existence problem for a DCA(4,q+1;q) with q≡2 (mod...
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