On tight spherical designs

Nebe, G.; Venkov, B.

doi:10.1090/S1061-0022-2013-01249-0

On tight spherical designs
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by G. Nebe and B. Venkov

St. Petersburg Math. J. 24 (2013), 485-491

DOI: https://doi.org/10.1090/S1061-0022-2013-01249-0

Published electronically: March 21, 2013

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Abstract:

Let $X$ be a tight $t$-design of dimension $n$, and let $t=5$ or $t=7$ (the open cases). An investigation of the lattice generated by $X$ by using arithmetic theory of quadratic forms allows one to exclude infinitely many values of $n$.

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