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- W4287704489 abstract "A finite subset $X$ on the unit sphere $mathbb{S}^{d-1}$ is called an $s$-distance set with strength $t$ if its angle set $A(X):={langle mathbf{x},mathbf{y}rangle : mathbf{x},mathbf{y}in X,mathbf{x}neqmathbf{y} }$ has size $s$, and $X$ is a spherical $t$-design but not a spherical $(t+1)$-design. In this paper, we consider to estimate the maximum size of such antipodal set for small $s$. First, we improve the known bound on $|X|$ for each even integer $sin[frac{t+5}{2}, t+1]$ when $tgeq 3$. We next focus on two special cases: $s=3, t=3$ and $s=4, t=5$. Estimating the size of $X$ for these two cases is equivalent to estimating the size of real equiangular tight frames (ETFs) and Levenstein-equality packings, respectively. We first improve the previous estimate on the size of real ETFs and Levenstein-equality packings. This in turn gives a bound on $|X|$ when $s=3, t=3$ and $s=4, t=5$, respectively." @default.
- W4287704489 created "2022-07-26" @default.
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- W4287704489 date "2020-07-28" @default.
- W4287704489 modified "2023-09-23" @default.
- W4287704489 title "Bounds on antipodal spherical designs with few angles" @default.
- W4287704489 hasPublicationYear "2020" @default.
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