The standard method for constructing generating vectors for good latticepoint sets is the component-by-component construction. Numerical experimentshave shown that the generating vectors found by these constructions sometimestend to have recurring components, which can lead to the problem of havingprojections with all lattice points lying on the main diagonal. In this paperwe combine methods of Dick and Kritzer to avoid this problem with a reducedfast component-by-component construction. That is, we give a variation of thestandard component-by-component construction which avoids repeated componentsand simultaneously results in a considerable speed-up in comparison to thestandard construction.
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