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

The classes of (u,m, e, s)-nets and (u, 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, e, s)-nets and (u, 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, e, s)-nets and present a new construction of such nets based on global function fields. © 2014 Elsevier Inc. All rights reserved.