  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.
