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Solving Rubik's cube in 40 quarter turns

Recently it has been discovered that the cube restricted to edges can be solved in at most 18 quarter turns. This calculation can be
found at http://www.cubeman.org .This means that given an arbitrary cube in the whole cube group one can solve the edges in at most 18 quarter turns. Once the edges are solved there are 44089920 possibilities for the corners. We prove that each of this configurations can be solved in at most 22 quarter turns. A list of all this configurations expressed in the generators can be found at: http://www.efd.lth.se/~f01sr/ under the link "Data file" (txt document). This list contains only representatives up to M-symmetry+inverse.