One important property that these fast double excitation generators rely on, is that the magnitude of the matrix element between two determinants, connected by a double excitation, does not depend on the involved determinants (details in Section 2). This property allows the determinant-independent precalculation of probability distributions and their efficient sampling. Algorithms for efficient excitation generation are also highly relevant for related methods such as selected-CI or FCI Fast Randomized Iteration (FCI-FRI).