2013/12/20 by Peter Kritzer, Kritzer, Peter, Harald Niederreiter +1
Mathematics · #11K31 #11K38 #65C05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11K31 #msc:11K38 #msc:65C05
paper · pdf · doi:10.48550/arxiv.1312.5855
arxiv created 2013/12/20 · arxiv updated 2013/12/23
The classes of (u,m,\bf e,s)-nets and (u,\bf 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,\bf e,s)-nets and (u,\bf 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,\bf e,s)-nets and present a new construction of such nets based on global function fields.