Research Article

A lattice without a basis of minimal vectors

J. H. Conwaya1 and Dr N. J. A. Sloanea2

a1 Department of Mathematics, Princeton University, Princeton, New Jersey 08544, U.S.A.

a2 Mathematical Sciences Research Center, AT&T Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A.


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.

(Received January 10 1994)

Key Words:

  • 11H99: NUMBER THEORY; Geometry of numbers.