As a final remark for possible future applications, we note that the Stochastic-GAS strategy can be utilized also for core-excitations, necessary in simulating X-ray diffraction spectroscopy. As for the conventional GAS strategy, core orbitals can be included in one of the GAS subspaces and constrain them to have a minimum number of holes. The advantage of Stochastic-GAS over conventional GAS is that in the former the GAS subspaces Definition 6.3 (Composition and supergroup index). We assume lexicographical decreasing order of the compositions and assign the composition index based on this order.