Mixed orthogonal arrays, $(u,m,\mathbf{e},s)$-nets, and $(u,\mathbf{e},s)$-sequences

We study the classes of $(u,m,\mathbf{e},s)$-nets and $(u,\mathbf{e},s)$-sequences, which are generalizations of $(u,m,s)$-nets and $(u,s)$-sequences, respectively. We show equivalence results that link the existence of $(u,m,{\bf e},s)$-nets and so-called mixed (ordered) orthogonal arrays, thereby generalizing earlier results by Lawrence, and Mullen and Schmid. We use this combinatorial equivalence principle to obtain new results on the possible parameter configurations of $(u,m,\mathbf{e},s)$-nets and $(u,{\bf e},s)$-sequences, which generalize in particular a result of Martin and Stinson.