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

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.