# A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy

## TL;DR

This paper introduces a faster method for constructing polynomial lattice point sets with low weighted star discrepancy by limiting the polynomial set size, leveraging rapidly decaying weights to reduce computational costs.

## Contribution

It proposes a reduced construction algorithm for polynomial lattice point sets that maintains low discrepancy while significantly lowering computational effort.

## Key findings

- Construction cost is substantially reduced.
- Maintains low weighted star discrepancy.
- Applicable to high-dimensional integration problems.

## Abstract

The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a component-by-component construction to ensure a small weighted star discre-pancy. Our aim is to significantly reduce the construction cost of such generating vectors by restricting the size of the set of polynomials from which we select the components of the vectors. To gain this reduction we exploit the fact that the weights of the spaces we consider decay very fast.