Author

Zi-Li Xu

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Preprint Sep 2026

Arithmetic Nonexistence Conditions for Tight Spherical $5$-Designs

We prove two arithmetic nonexistence conditions for tight spherical $5$-designs in dimension $(2m+1)^2-2$. Let $m$ be a positive even integer satisfying $\nu_2(m(m+1))\leq5$, where $\nu_p(a)$ denotes the exponent of the prime $p$ in the positive integer $a$. We show that such a design does not exist if either (i) $m\eq...

Zi-Li Xu · 0 citations

Preprint Sep 2026

Spherical $t$-Designs on $\mathbb S^2$ with $54t^2$ Points

We prove that, for every integer $t\geq 1$, the unit two-sphere admits a spherical $t$-design consisting of exactly $54t^2$ points. More generally, such a design exists with exactly $6q^2$ points for every integer $q\geq 3t$. The proof builds on the topological degree method of Bondarenko, Radchenko and Viazovska, usin...

Zhi-Qiang Xu, Zi-Li Xu · 0 citations