Spherical designs and lattices
arXiv:1111.0772 · doi:10.1007/s13366-013-0155-5
Abstract
In this article we prove that integral lattices with minimum <= 7 (or <= 9) whose set of minimal vectors form spherical 9-designs (or 11-designs respectively) are extremal, even and unimodular. We furthermore show that there does not exist an integral lattice with minimum <=11 which yields a 13-design.
The final publication is available at http://link.springer.com/article/10.1007%2Fs13366-013-0155-5