Antipodality of spherical designs with odd harmonic indices

Ryutaro Misawa, Akihiro Munemasa, Masanori Sawa

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 pro…