We recently submitted the manuscript

- J. Baldeaux, J. Dick, J. Greslehner, and F. Pillichshammer, Construction Algorithms for Higher Order Polynomial Lattice Rules. Submitted 2010.

This paper fits into the work on higher order quasi-Monte Carlo rules which started with [22] and [31]. It can be viewed as the higher order extension of [7], where classical polynomial lattice rules were considered.

**1. Construction Algorithms **

As stated in the title of the manuscript, we present construction algorithms for higher order polynomial lattice rules. The construction is based on the worst-case error rather than the quality parameter . This allows us to find good higher order polynomial lattice rules for weighted function spaces. It also presents a feasible alternative to the direct construction introduced in [31] (and [22] for the periodic case).

We use a variety of approaches to achieve our results. Continue reading