Semidefinite Programming Bounds For Spherical Three-distance Sets
| Autor: | Liu, Feng-Yuan, Yu, Wei-Hsuan |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | A spherical three-distance set is a finite collection $X$ of unit vectors in $\mathbb{R}^{n}$ such that for each pair of distinct vectors has three inner product values. We use the semidefinite programming method to improve the upper bounds of spherical three-distance sets for several dimensions. We obtain better bounds in $\mathbb{R}^7$, $\mathbb{R}^{20}$, $\mathbb{R}^{21}$, $\mathbb{R}^{23}$, $\mathbb{R}^{24}$ and $\mathbb{R}^{25}$. In particular, we prove that maximum size of spherical three-distance sets is $2300$ in $\mathbb R^{23}$. Comment: 10 pages |
| Databáze: | arXiv |
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