Rank 72 high minimum norm lattices

  title={Rank 72 high minimum norm lattices},
  author={Robert L. Griess},
Given a polarization of an even unimodular lattice and integer k ≥ 1, we define a family of unimodular lattices L(M, N, k). Of special interest are certain L(M,N, 3) of rank 72. Their minimum norms lie in {4, 6, 8}. Norms 4 and 6 do occur. Consequently, 6 becomes the highest known minimum norm for rank 72 even unimodular lattices. We discuss how norm 8 might occur for such a L(M,N, 3). We note a few L(M,N, k) in dimensions 96, 120 and 128 with moderately high minimum norms.