Propagation rules for (u,m,e,s)-nets and (u,e,s)-sequences

Abstract

The classes of $(u,m,\mathbf{e},s)$-nets and $(u,\mathbf{e},s)$-sequences were recently introduced by Tezuka, and in a slightly more restrictive form by Hofer and Niederreiter. We study propagation rules for these point sets, which state how one can obtain $(u,m,\mathbf{e},s)$-nets and $(u,\mathbf{e},s)$-sequences with new parameter configurations from existing ones. In this way, we show generalizations and extensions of several well-known construction methods that have previously been shown for $(t,m,s)$-nets and $(t,s)$-sequences. We also develop a duality theory for digital $(u,m,\mathbf{e},s)$-nets and present a new construction of such nets based on global function fields.