Construction of Digital Nets Based on Propagation Rules for OOAs

(t, m, s)-nets are a powerful tool for the generation of low-discrepancy point sets. We find nets with improved parameters using a coding-theoretic approach, starting with an orthogonal array (dual of a linear code) and embedding it in a net. The innovation of our approach is that propagation rules for OOAs are applied halfway through the embedding process. To this end many propagation rules have been generalized from the setting of orthogonal arrays to OOAs. According to MINT [1], the online database of (t, m, s)-net parameters at mint.sbg.ac.at, more than 100 nets with previously unknown parameters have been found using this method. Copyright line will be provided by the publisher 1 Definitions and Earlier Results (t, m, s)-nets [2] (see also the monograph [3]) are a powerful tool for the generation of low-discrepancy point sets: Definition 1.1 A (t, m, s)-net in base b is a multiset N of bm points in [0, 1)s such that every interval of the form∏s i=1 ai/