论文标题
球形三距离集的半决赛编程范围
Semidefinite Programming Bounds For Spherical Three-distance Sets
论文作者
论文摘要
球形三距离集是一个有限的集合$ x $的单位向量的$ \ mathbb {r}^{n} $，因此，对于每对不同的矢量，有三个内部产品值。我们使用半决赛编程方法来改善几个维度的球形三距离集的上限。我们获得$ \ Mathbb {r}^7 $，$ \ mathbb {r}^{20} $，$ \ Mathbb {r}^{21} $，$ \ Mathbb {r}^{R}^{23} $，$ \ MATHBB {23} $，$ \ MATHBB {23} $，$ \ MATHBB {RAMTHBB {23}，特别是，我们证明，球形三距离集的最大尺寸为$ 2300 $ in $ \ MATHBB R^{23} $。
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 $\mathbb R^{23}$.
