On combined component-by-component constructions of lattice point sets

TL;DR

This paper introduces a modified component-by-component construction method for lattice point sets that prevents recurring components, improves the distribution of points, and accelerates the construction process.

Contribution

It presents a novel variation of the standard method that avoids repeated components and enhances computational efficiency.

Findings

Reduces repeated components in generating vectors

Speeds up the construction process

Improves the quality of lattice point sets

Abstract

The standard method for constructing generating vectors for good lattice point sets is the component-by-component construction. Numerical experiments have shown that the generating vectors found by these constructions sometimes tend to have recurring components, which can lead to the problem of having projections with all lattice points lying on the main diagonal. In this paper we combine methods of Dick and Kritzer to avoid this problem with a reduced fast component-by-component construction. That is, we give a variation of the standard component-by-component construction which avoids repeated components and simultaneously results in a considerable speed-up in comparison to the standard construction.