A solved Sudoku will remain valid under the actions of the validity preserving transformations (see also Jarvis). By carefully counting the number of invariant grids for each transformation one can compute the number of essentially different Sudoku grids (see above). Similar methods have been applied to sudoku grids of other dimensions; the results are summarized in the table below. For square block grids the transposition transformation may or may not (in italics below) be included in the VPT (symmetry) group. The number of essentially different grids can also be estimated by dividing the total number of grids (either known or estimated) by the size of the VPT group (which is easily computed), which essentially assumes the number of automorphic sudokus is negligible. The numbers for 2 × "n" blocks (2"n" × 2"n" grids) are listed in .