  We further pursue an approach to the sign problem of quantum chromodynamics
at nonzero chemical potential, in which configurations of the lattice path
integral are gathered into subsets. In the subset construction we multiply each
temporal link by center elements independently and in a first step neglect the
gauge action. The positivity of the subset weights -- shown for 0+1 dimensions
in an earlier study -- extends to larger lattices: for two sites in the
temporal direction and arbitrary spatial extent we give a proof of the
positivity by decomposing the subset weight in positive summands. From
numerical evidence we conjecture that the positivity persists on larger
lattices and that the gauge action can be reintroduced through mild
reweighting. First results on the quark number obtained with this method in two
dimensions are shown as well.
