Constructions of new orthogonal arrays and covering arrays of strength three

A covering array of size N, strength t, degree k, and order v, or a CA(N;t,k,v) in short, is a k×N array on v symbols. In every t×N subarray, each t-tuple column vector occurs at least once. When ‘at least’ is replaced by ‘exactly’, this defines an orthogonal array, OA(t,k,v). A difference covering array, or a DCA(k,n;v), over an abelian group G of order v is a k×n array (aij) (1⩽i⩽k, 1⩽j⩽n) with entries from G, such that, for any two distinct rows l and h of D (1⩽l