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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Böttcher, Albrecht Fukshansky, Lenny Garcia, Stephan Ramon and Maharaj, Hiren 2015. On Lattices Generated by Finite Abelian Groups. SIAM Journal on Discrete Mathematics, Vol. 29, Issue. 1, p. 382.

    Sha, Min 2015. On the lattices from elliptic curves over finite fields. Finite Fields and Their Applications, Vol. 31, p. 84.

    Beye, Florian 2014. Chiral four-dimensional heterotic covariant lattices. Journal of High Energy Physics, Vol. 2014, Issue. 11,

    MARTINET, JACQUES and SCHÜRMANN, ACHILL 2012. BASES OF MINIMAL VECTORS IN LATTICES, III. International Journal of Number Theory, Vol. 08, Issue. 02, p. 551.


A lattice without a basis of minimal vectors

  • J. H. Conway (a1) and N. J. A. Sloane (a2)
  • DOI:
  • Published online: 01 February 2010

It is shown that in all dimensions n ≥ 11 there exists a lattice which is generated by its minimal vectors but in which no set of n minimal vectors forms a basis.

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1.J. H. Conway and N. J. A. Sloane . Sphere Packings, Lattices and Groups, Second edition (Springer-Verlag, New York, 1993).

6.M. Senechal . Introduction to lattice geometry. In From Number Theory to Physics (edited by M. Waldschmidt et al.) (Springer-Verlag, New York, 1992), pp. 476495.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
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