**New Sphere Packings in Dimensions 9-15**, J. Leech and N. J. A. Sloane,*Bull. Amer. Math. Soc.*, 76 (1970), pp. 1006-1010.**New Sphere Packings in More Than Thirty-Two Dimensions**, J. Leech and N. J. A. Sloane,*Proceedings Second Chapel Hill Conference on Combinatorial Mathematics and its Applications*, Univ. of North Carolina, Chapel Hill, NC, 1970, pp. 345-355.**Sphere Packing and Error-Correcting Codes**, J. Leech and N. J. A. Sloane,*Canad. J. Math.*, 23 (1971), pp. 718-745, A revised version appears as Chapter 5 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.**Sphere Packings Constructed from BCH and Justesen Codes**, N. J. A. Sloane,*Mathematika*, 19 (1972), pp. 183-190.**Upper Bounds for Modular Forms, Lattices, and Codes**, C. L. Mallows, A. M. Odlyzko and N. J. A. Sloane,*J. Algebra*, 36 (1975), pp. 68-76.**Codes over GF(4) and Complex Lattices**, N. J. A. Sloane,*J. Algebra*, 52 (1978), pp. 168-181.**Binary Codes, Lattices, and Sphere-Packings**, N. J. A. Sloane,*Combinatorial Surveys: Proceedings of the Sixth British Combinatorial Conference*, P. J. Cameron (editor), Academic Press, NY, 1977, pp. 117-164, Russian translation in ``Mathematics: New in Foreign Science'', Vol. 19 (1980), pp. 219-249.**Extremal Self-Dual Lattices Exist Only in Dimensions 1-8, 12, 14, 15, 23 and 24**, J. H. Conway, A. M. Odlyzko and N. J. A. Sloane,*Mathematika*, 25 (1978), pp. 36-43, A revised version appears as Chapter 19 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.**Self-Dual Codes and Lattices**, N. J. A. Sloane,*Relations Between Combinatorics and Other Parts of Mathematics.*, Proc. Symp. Pure Math., Vol. 34, American Mathematical Society, Providence, RI, 1979, pp. 273-308.**Tables of Sphere Packings and Spherical Codes**, N. J. A. Sloane,*IEEE Trans. Information Theory*, IT-27 (1981), pp. 327-338.**On Exceptions of Integral Quadratic Forms**, A. M. Odlyzko and N. J. A. Sloane,*J. Reine Angew. Math.*, 321 (1981), pp. 212-216.**On the Enumeration of Lattices of Determinant One**, J. H. Conway and N. J. A. Sloane,*J. Number Theory*, 15 (1982), pp. 83-94.**Voronoi Regions of Lattices, Second Moments of Polytopes, and Quantization**, J. H. Conway and N. J. A. Sloane,*IEEE Trans. Information Theory*, IT-28 (1982), pp. 211-226, A revised version appears as Chapter 21 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988. Reprinted in ``Vector Quantization'', H. Abut, Ed., IEEE Press, NY, 1990, pp. 118-133.**Fast Quantizing and Decoding Algorithms for Lattice Quantizers and Codes**, J. H. Conway and N. J. A. Sloane,*IEEE Trans. Information Theory*, IT-28 (1982), pp. 227-232, Reprinted in ``Vector Quantization'', H. Abut, Ed., IEEE Press, NY, 1990, pp. 134-139.**Twenty-Three Constructions for the Leech Lattice**, J. H. Conway and N. J. A. Sloane,*Proc. Roy. Soc. London, Series A*, 381 (1982), pp. 275-283, A revised version appears as Chapter 24 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.**The Covering Radius of the Leech Lattice**, J. H. Conway, R. A. Parker and N. J. A. Sloane,*Proc. Roy. Soc. London, Series A*, 380 (1982), pp. 261-290, A revised version appears as Chapter 23 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.**Recent Bounds for Sphere Packings and Related Problems Obtained by Linear Programming and Other Methods**, N. J. A. Sloane,*Papers in Analysis, Algebra and Statistics, Contemporary Math., Vol. 9*, R. Lidl (editor), Amer. Math. Soc., Providence, RI, 1982, pp. 153-185, A revised version appears as Chapter 9 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.**Lorentzian Forms for the Leech Lattice**, J. H. Conway and N. J. A. Sloane,*Bull. Amer. Math. Soc.*, 6 (1982), pp. 215-217, A revised version appears as Chapter 26 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.**On a Problem of Ryskov Concerning Lattice Coverings**, R. P. Bambah and N. J. A. Sloane,*Acta Arithmetica*, 42 (1982), pp. 107-109.**A Theta-Function Identity for Nonlattice Packings**, A. M. Odlyzko and N. J. A. Sloane,*Studia Scient. Math. Hungarica*, 5 (1980), pp. 461-465.**Laminated Lattices**, J. H. Conway and N. J. A. Sloane,*Annals of Math.*, 116 (1982), pp. 593-620, A revised version appears as Chapter 6 of ``Sphere Packings, Lattices and Groups'' by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.**New Lattice Packings of Spheres**, E. S. Barnes and N. J. A. Sloane,*Canad. J. Math.*, 35 (1983), pp. 117-130.**The Optimal Lattice Quantizer in Three Dimensions**, E. S. Barnes and N. J. A. Sloane,*SIAM J. Algebraic Discrete Methods*, 4 (1983), pp. 30-41.**The Unimodular Lattices of Dimension up to 23 and the Minkowski-Siegel Mass Constants**, J. H. Conway and N. J. A. Sloane,*European J. Combinatorics*, 3 (1982), pp. 219-231.**Further Lattice Packings in High Dimensions**, A. Bos, J. H. Conway and N. J. A. Sloane,*Mathematika*, 29 (1982), pp. 171-180.**A Fast Encoding Method for Lattice Codes and Quantizers**, J. H. Conway and N. J. A. Sloane,*IEEE Trans. Information Theory*, IT-29 (1983), pp. 820-824.**Complex and Integral Laminated Lattices**, J. H. Conway and N. J. A. Sloane,*Trans. Amer. Math. Soc.*, 280 (1983), pp. 463-490.**The Coxeter-Todd Lattice, The Mitchell Group and Related Sphere Packings**, J. H. Conway and N. J. A. Sloane,*Math. Proc. Comb. Phil. Soc.*, 93 (1983), pp. 421-440.**On the Voronoi Regions of Certain Lattices**, J. H. Conway and N. J. A. Sloane,*SIAM J. Algebraic Discrete Methods*, 5 (1984), pp. 294-305.**The Packing of Spheres**, N. J. A. Sloane,*Scientific American*, 250 (January, 1984), pp. 116-125, (Also ``Les Empilements de Spheres'', Pour la Science, Mars, 1984, pp. 44-55; ``Kugelpackungen im Raum'', Spektrum der Wissenschaft, March, 1984; ``Empaquetamiento de Esferas'', Investigacion y Ciencia, March 1984, pp. 88-99.).**On the Classification of Integral Quadratic Forms**, J. H. Conway and N. J. A. Sloane,*Sphere Packings, Lattices and Groups*, Springer-Verlag, NY, Chapter 15, 1988, pp. 352-405.**A Lower Bound on the Average Error of Vector Quantizers**, J. H. Conway and N. J. A. Sloane,*IEEE Trans. Information Theory*, IT-31 (1985), pp. 106-109.**Soft Decoding Techniques for Codes and Lattices, Including the Golay Code and the Leech Lattice**, J. H. Conway and N. J. A. Sloane,*IEEE Trans. Information Theory*, IT-32 (1986), pp. 41-50.**Theta Series and Magic Numbers for Close-Packed Spherical Clusters**, N. J. A. Sloane and B. K. Teo,*J. Chem. Phys.*, 83 (1985), pp. 6520-6534.**New Trellis Codes Based on Lattices and Cosets**, A. R. Calderbank and N. J. A. Sloane,*IEEE Trans. Information Theory*, IT-33 (1987), pp. 177-195.**Atomic Arrangements and Electronic Requirements for Close-Packed Circular and Spherical Clusters**, B. K. Teo and N. J. A. Sloane,*Inorganic Chemistry*, 25 (1986), pp. 2315-2322.**An Eight-Dimensional Trellis Code**, A. R. Calderbank and N. J. A. Sloane,*Proc. IEEE*, 74 (1986), pp. 757-759.**An Improvement to the Minkowski-Hlawka Bound for Packing Superballs**, [note: Fig. 1 is in a in separate file] J. A. Rush and N. J. A. Sloane,*Mathematika*, 34 (1987), pp. 8-18.**Theta-Series and Magic Numbers for Diamond and Certain Ionic Crystal Structures**, [note: Fig. 1 is in a separate file] N. J. A. Sloane,*J. Math. Phys.*, 28 (1987), pp. 1653-1657.**Penny-Packing and Two-Dimensional Codes**, [note: Fig. 1 , Fig. 2 , Fig. 3 , Fig. 4 , Fig. 5 , Fig. 6 are in separate files] R. L. Graham and N. J. A. Sloane,*Discrete and Comput. Geom.*, 5 (1990), pp. 1-11.**Multi-Dimensional Coding For Error Reduction**, A. R. Calderbank and N. J. A. Sloane, U. S. Patent No. 4,581,601, April 8, 1986.**A Highly Symmetric Four-Dimensional Quasicrystal**, V. Elser and N. J. A. Sloane,*J. Phys. A.*, 20 (1987), pp. 6161-6168.**Low-Dimensional Lattices I: Quadratic Forms of Small Determinant**, J. H. Conway and N. J. A. Sloane,*Proc. Royal Soc. London, Series A*, 418 (1988), pp. 17-41.**Low-Dimensional Lattices II: Subgroups of GL(n, Z)**, J. H. Conway and N. J. A. Sloane,*Proc. Royal Soc. London, Series A*, 419 (1988), pp. 29-68.**Low-Dimensional Lattices III: Perfect Forms**, J. H. Conway and N. J. A. Sloane,*Proc. Royal Soc. London, Series A*, 418 (1988), pp. 43-80.**Low-Dimensional Lattices IV: The Mass Formula**, J. H. Conway and N. J. A. Sloane,*Proc. Royal Soc. London, Series A*, 419 (1988), pp. 259-286.**Low-Dimensional Lattices V: Integral Coordinates for Integral Lattices**, J. H. Conway and N. J. A. Sloane,*Proc. Royal Soc. London, Series A*, 426 (1989), pp. 211-232.**A New Upper Bound for the Minimum of an Integral Lattice of Determinant One**, J. H. Conway and N. J. A. Sloane,*Bull. Amer. Math. Soc.*, 23 (1990), pp. 383-387, Erratum: volume 24 (April 1991), p. 479.**Multi-Dimensional Coding for Error Reduction**, A. R. Calderbank and N. J. A. Sloane, U. S. Patent Re. 33,041, August 29, 1989.**Lattices with Few Distances**, [note: some tables are in a separate file] J. H. Conway and N. J. A. Sloane,*J. Number Theory*, 39 (1991), pp. 75-90, Also DIMACS Technical Report 90-77, December 1990.**The Cell Structures of Certain Lattices**, [note: Fig. 1a , Fig. 1b , Fig. 2a , Fig. 2b , Fig. 3a , Fig. 3b , Fig. 4 , Fig. 5 , Fig. 6 , Fig. 7 , Fig. 8 , Fig. 9 , Fig. 10 , Fig. 11 , Fig. 12 , Fig. 13 , Fig. 14 , Fig. 15 , Fig. 16a , Fig. 16b , Fig. 17 , Fig. 18 , Fig. 19 , Fig. 20 , Fig. 21 , Fig. 22 , Fig. 23 , Fig. 24 , Fig. 25 , Fig. 26 , are in separate files] J. H. Conway and N. J. A. Sloane,*Miscellanea mathematica*, P. Hilton, F. Hirzebruch and R. Remmert (editors), Springer-Verlag, NY, 1991, pp. 71-107, Also DIMACS Technical Report 91-5, February 1991.**On the Covering Multiplicity of Lattices**, [note: Fig. 1 , Fig. 2 and Fig. 4 are in separate files] J. H. Conway and N. J. A. Sloane,*Discrete and Computational Geometry*, 8 (1992), pp. 109-130.**Trellis Coding Arrangement**, A. R. Calderbank and N. J. A. Sloane, U. S. Patent No. 4,939,555, July 3, 1990.**Low-Dimensional Lattices VI: Voronoi Reduction of Three-Dimensional Lattices**, J. H. Conway and N. J. A. Sloane,*Proc. Royal Soc. London, Series A*, 436 (1992), pp. 55-68.**Four-Dimensional Lattices With the Same Theta Series**, J. H. Conway and N. J. A. Sloane,*Duke Math. J.*, 66 (International Mathematics Research Notices Number 4) (1992), pp. 93-96.**Sphere Packings, Lattices and Groups (Second Edition)**, J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1993, 679 pp.**On Lattices Equivalent to Their Duals**, J. H. Conway and N. J. A. Sloane,*J. Number Theory*, 48 (1994), pp. 373-382, Also DIMACS Technical Report 93-88, December 1993.**D4, E8, Leech and Certain Other Lattices are Symplectic**, J. H. Conway and N. J. A. Sloane, Appendix to P. Buser and P. Sarnak, "On the Period Matrix of a Riemann Surface of Large Genus", Inventiones Math., vol. 117 (1994), pp. 27-56. Also DIMACS Technical Report 93-55, August 1993.**A Lattice Without a Basis of Minimal Vectors**, J. H. Conway and N. J. A. Sloane,*Mathematika*, 42 (1995), pp. 175-177.**Minimal-Energy Clusters of Hard Spheres**, [note: Fig. 11 , Fig. 12 and "photos" of the putatively optimal clusters of 4 to 10 and 13 to 20 spheres are in separate files] N. J. A. Sloane, R. H. Hardin, T. S. Duff and J. H. Conway,*Discrete Computational Geom.*, 14 (1995), pp. 237-259.**What Are All the Best Sphere Packings in Low Dimensions?**, J. H. Conway and N. J. A. Sloane,*Discrete and Computational Geometry (Laszlo Fejes Toth Festschrift)*, 13 (1995), pp. 383-403.**The Antipode Construction for Sphere Packings**, J. H. Conway and N. J. A. Sloane,*Inventiones mathematica*, 123 (1996), pp. 309-313.**On Sublattices of the Hexagonal Lattice**, M. Bernstein, N. J. A. Sloane and P. E. Wright,*Discrete Math.*, 170 (1997), pp. 29-39.**Double Circulant Codes over Z4 and Even Unimodular Lattices**, A. R. Calderbank and N. J. A. Sloane,*J. Algebraic Combinatorics*, 6 (1997), pp. 119-131.**The Ternary Golay Code, the Integers Mod 9 and the Coxeter-Todd Lattice**, A. R. Calderbank and N. J. A. Sloane,*IEEE Trans. Inform. Theory*, 42 (1996), pp. 636-637. (Unfortunately this paper is wrong: the lattice is not K_12)**Some Lattices Obtained from Riemann Surfaces**, M. Bernstein and N. J. A. Sloane,*Extremal Riemann Surfaces (Contemporary Math. Vol. 201)*, J. R. Quine and P. Sarnak (editors), Amer. Math. Soc., Providence, RI, 1997, pp. 29-32.**Low-Dimensional Lattices VII: Coordination Sequences**[postscript, pdf], J. H. Conway and N. J. A. Sloane,*Proc. Royal Soc. London, Series A*, 453 (1997), pp. 2369-2389.**Kugelpackungen im Raum**, N. J. A. Sloane,*Moderne Mathematik*, G. Faltings (editor), Spektrum Akademischer Verlag, Heidelberg, Germany, 1996, pp. 112-123.**Packing Lines, Planes, etc.: Packings in Grassmannian Space**[postscript, pdf], J. H. Conway, R. H. Hardin and N. J. A. Sloane,*Experimental Math.*, 5 (1996), pp. 139-159.**A Family of Optimal Packings in Grassmannian Manifolds**[postscript, pdf], P. W. Shor and N. J. A. Sloane,*J. Algebraic Combinatorics*, 7 (1998), pp. 157-163.**A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces**[postscript, pdf], A. R. Calderbank, R. H. Hardin, E. M. Rains, P. W. Shor and N. J. A. Sloane,*J. Algebraic Combinatorics*, 9 (1999), pp. 129-140.**The Shadow Theory of Modular and Unimodular Lattices**, E. M. Rains and N. J. A. Sloane,*J. Number Theory*, 73 (1998), pp. 359-389.**A Note on Optimal Unimodular Lattices**[postscript, pdf], J. H. Conway and N. J. A. Sloane,*J. Number Theory*, 72 (1998), pp. 357-362.-
**Database of Lattices**G. Nebe and N. J. A. Sloane, Published electronically at http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/. **Packing Planes in Four Dimensions and Other Mysteries**[postscript, pdf], N. J. A. Sloane,*Algebraic Combinatorics and Related Topics (Yamagata 1997)*, E. Bannai, M. Harada and M. Ozeki (editors), Yamagata University, Faculty of Science, Department of Mathematics, 1998, 1999.**On Kissing Numbers in Dimensions 32 to 128**[postscript, pdf], Y. Edel, E. M. Rains and N. J. A. Sloane, Elect. J. Combinatorics 5(1), paper R22 (1998).**The Sphere Packing Problem**[postscript, pdf], N. J. A. Sloane, Proceedings Internat. Congress Math. Berlin 1998, Documenta Mathematika, III (1998), pp. 387-396.**Kepler's Conjecture Confirmed**[postscript, pdf], N. J. A. Sloane,*Nature*, 395 (October 1, 1998), pp. 435-436.**On the Existence of Similar Sublattices**[postscript, pdf], J. H. Conway, E. M. Rains and N. J. A. Sloane,*Canad. J. Math.*, 1999 submitted.