Zi-Li Xu

activity

20202026

collaborators

4 papers

math.CO2026

Arithmetic Nonexistence Conditions for Tight Spherical $5$ -Designs

Zili Xu

We prove two arithmetic nonexistence conditions for tight spherical $5$ -designs in dimension $(2 m + 1)^{2} - 2$ . Let $m$ be a positive even integer satisfying $ν_{2} (m (m + 1)) \leq 5$ , where $…

math.CO2025

Existence and nonexistence of spherical $5$ -designs of minimal type

Sho Suda, Zili Xu, Wei-Hsuan Yu

This paper investigates the existence and properties of spherical $5$ -designs of minimal type. We focus on two cases: tight spherical $5$ -designs and antipodal spherical $4$ -distan…

cs.IT2024

Stability in Phase Retrieval: Characterizing Condition Numbers and the Optimal Vector Set

Yu Xia, Zhiqiang Xu, Zili Xu

In this paper, we primarily focus on analyzing the stability property of phase retrieval by examining the bi-Lipschitz property of the map $Φ_{\boldsymbol{A}}(\boldsymbol{x})=|\bol…

math.CO2020

Bounds on antipodal spherical designs with few angles

Zhiqiang Xu, Zili Xu, Wei-Hsuan Yu

A finite subset $X$ on the unit sphere $S^{d - 1}$ is called an $s$ -distance set with strength $t$ if its angle set $A(X):=\{\langle \mathbf{x},\mathbf{y}\rangle : \mathbf{x…

Arithmetic Nonexistence Conditions for Tight Spherical 5-Designs

Existence and nonexistence of spherical 5-designs of minimal type

Stability in Phase Retrieval: Characterizing Condition Numbers and the Optimal Vector Set

Bounds on antipodal spherical designs with few angles

Arithmetic Nonexistence Conditions for Tight Spherical $5$ -Designs

Existence and nonexistence of spherical $5$ -designs of minimal type