A Classification of Lattice Rules Using the Reciprocal Lattice Generator Matrix

..........................................................................................................................................1 1. Background................................................................................................................................1 2. The Upper Triangular Lattice Form (utlt) of B .......................................................................... 4 3. The Good Lattices......................................................................................................................5 4. Some New Lattice Rules............................................................................................................5 References.......................................................................................................................................7 Appendix A: The Algorithm..........................................................................................................9 Appendix B: Projections.............................................................................................................11 Appendix C: The Uniqueness of the Representation....................................................................13 Appendix D: The Lower Triangular Lattice Form .................................................... 14 Appendix E: The Inverse of B......................................................................................................15