Although the new dependency on i sg (D i ) increases the number of probability distributions that have to be generated and stored, the direct dependency on the individual Slater deter-minants is circumvented, making GAS-PCHB a practical tool of general applicability. In the next section the scaling of the algorithm will be discussed together with some examples that show the practical limitations bound to the dependency of p(AB; IJ; i sg ) on the number of supergroups. However, we can anticipate that since there are much fewer supergroups than determinants, the different probability distributions can in most of the practical cases be precomputed and stored.