Antipodality of spherical designs with odd harmonic indices

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

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Publication Details

Journal
Discrete Mathematics
Published
2026-01-14
DOI
https://doi.org/10.1016/j.disc.2026.114978
Primary Topic
Mathematical Approximation and Integration
Type
article
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article

Antipodality of spherical designs with odd harmonic indices

Masanori Sawa, Akihiro Munemasa, R. Misawa
Discrete Mathematics
Mathematical Approximation and Integration
article

Antipodality of spherical designs with odd harmonic indices

Masanori Sawa, Akihiro Munemasa, R. Misawa
article en

Abstract

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

Discrete MathematicsVol. 349(6)
Tohoku University (JP), Kobe University (JP)
Sustainable cities and communities
Openalex Percentile: Top 85%
Mathematical Approximation and Integration
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Antipodality of spherical designs with odd harmonic indices — Masanori Sawa, Akihiro Munemasa, et al. · Discrete Mathematics (2026) | TGRS Research Map | TGRS