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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 Carlointegration algorithms. Essential tools in finding such point sets of highquality are propagation rules, which make it possible to generate new higherorder nets from existing higher order nets and even classical $(t,m,s)$-nets.Such propagation rules for higher order nets were first considered by theauthors in [J. Dick, P. Kritzer. Duality theory and propagation rules forgeneralized digital nets. Math. Comp. 79, 993--1017, 2010] and furtherdeveloped in [J. Baldeaux, J. Dick, F. Pillichshammer. Duality theory andpropagation rules for higher order nets. Discrete Math. 311, 362--386, 2011].In [E.L. Blokh, V.V. Zyablov. Coding of generalized concatenated codes.Problems of Information Transmission, 10, 218--222, 1974] Blokh and Zyablovestablished a very general propagation rule for linear codes. This propagationrule has been extended to $(t,m,s)$-nets by Sch\"urer and Schmid in [R.Sch\"{u}rer, W.Ch. Schmid. \textit{MinT---the database of optimal net, code,OA, and OOA parameters}. Available at: \texttt{http://mint.sbg.ac.at}]. In thispaper we show that this propagation rule can also be extended to higher ordernets. Examples indicate that this propagation rule yields new higher order netswith significantly higher quality.

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