  The component-by-component construction is the standard method of finding
good lattice rules or polynomial lattice rules for numerical integration.
Several authors have reported that in numerical experiments the generating
vector sometimes has repeated components. We study a variation of the classical
component-by-component algorithm for the construction of lattice or polynomial
lattice point sets where the components are forced to differ from each other.
This avoids the problem of having projections where all quadrature points lie
on the main diagonal. Since the previous results on the worst-case error do not
apply to this modified algorithm, we prove such an error bound here. We also
discuss further restrictions on the choice of components in the
component-by-component algorithm.
