An Optimal Odd Unimodular Lattice in Dimension 72
  It is shown that if there is an extremal even unimodular lattice in dimension 72, then there is an optimal odd unimodular lattice in that dimension. Hence, the first example of an optimal odd unimodular lattice in dimension 72 is constructed from the extremal even unimodular lattice which has been recently found by G. Nebe. 
Masaaki Harada, Tsuyoshi Miezaki
math.CO math.NT