A higher order Blokh–Zyablov propagation rule for higher order nets

Higher order nets were introduced by Dick as a generalisation of classical (t,m,s)-nets, which are point sets frequently used in quasi-Monte Carlo integration algorithms. Essential tools in finding such point sets of high quality are propagation rules, which make it possible to generate new higher order nets from existing higher order nets and even classical (t,m,s)-nets. Such propagation rules for higher order nets were first considered by Dick and Kritzer (2010) [8], and further developed in Baldeaux et al. (2011) [2], . Blokh and Zyablov (1974) [4], established a very general propagation rule for linear codes. This propagation rule has been extended to (t,m,s)-nets by Schürer and Schmid (2012) [18]. In this paper we show that this propagation rule can also be extended to higher order nets. Examples indicate that this propagation rule yields new higher order nets with significantly higher quality.