Abstract
In this article we prove that integral lattices with minimum \(\le 7\) (or \(\le 9\)) 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 \(\le 11\) which yields a \(13\)-design.
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I would like to thank G. Nebe, my supervisor, for helpful comments.
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Nossek, E. Spherical designs and lattices. Beitr Algebra Geom 55, 25–31 (2014). https://doi.org/10.1007/s13366-013-0155-5
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DOI: https://doi.org/10.1007/s13366-013-0155-5