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arXiv · 2410.09471

Antipodality of spherical designs with odd harmonic indices

Ryutaro Misawa·Akihiro Munemasa·Masanori Sawa
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Abstract

We determine the smallest size of a non-antipodal spherical design with harmonic indices $\{1,3,\dots,2m-1\}$ to be $2m+1$, where $m$ is a positive integer. This is achieved by proving an analogous result for interval designs.

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Ryutaro Misawa, Akihiro Munemasa, Masanori Sawa. 2026-01-05. Antipodality of spherical designs with odd harmonic indices. https://arxiv.org/abs/2410.09471

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