Spherical designs and lattices

Details Spherical designs and lattices Spherical designs and lattices

2011-11-03

arxiv.org/abs/1111.0772v1

Mathematics

Number Theory

Scientific paper

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.

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