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

TL;DR

This paper explores generalized $(u,m,{f e},s)$-nets and sequences, establishing their equivalence with mixed orthogonal arrays and deriving new parameter constraints, thus broadening the theoretical understanding of these combinatorial structures.

Contribution

It introduces a unifying equivalence between generalized nets and mixed orthogonal arrays, extending previous results and providing new parameter bounds.

Findings

Established equivalence between $(u,m,{f e},s)$-nets and mixed orthogonal arrays.

Derived new constraints on parameters of generalized nets and sequences.

Extended prior results by Martin and Stinson.

Abstract

We study the classes of $(u,m,{\bf e},s)$-nets and $(u,{\bf e},s)$-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 $(u,m,{\bf e},s)$-nets and $(u,{\bf e},s)$-sequences, which generalize in particular a result of Martin and Stinson.