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arXiv · 2609.36725

Arithmetic Nonexistence Results for Tight Spherical $5$-Designs

Zili Xu
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Abstract

We prove two arithmetic nonexistence criteria for tight spherical $5$-designs in dimension $(2m+1)^2-2$ with $m$ even. Together, they recover the applicable criteria of Bannai-Munemasa-Venkov and Nebe-Venkov while covering parameters excluded by neither earlier result. Examples include $m=16,100$ under the first criterion and $m=96,168$ under the second. The proofs combine lattice moment identities, finite Gauss sums, and a determinant calculation modulo $3$.

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Zili Xu. 2026-09-29. Arithmetic Nonexistence Results for Tight Spherical $5$-Designs. https://arxiv.org/abs/2609.36725

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