A Note on Projecting the Cubic Lattice

The theorem is at first surprising, since A has ( n+1 2 ) degrees of freedom, whereas v has only n degrees of freedom (for the explanation see the remark following the proof of Theorem 2). The problem arises from a question in communication theory (see §5), which calls for projections Λv with high packing density. Since both the determinant and minimal norm of a lattice are continuous functions of the entries in the Gram matrix, so is the packing density.1 The theorem