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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 innerproduct values. We use the semidefinite programming method to improve the upperbounds of spherical three-distance sets for several dimensions. We obtainbetter bounds in $\mathbb{R}^7$, $\mathbb{R}^{20}$, $\mathbb{R}^{21}$,$\mathbb{R}^{23}$, $\mathbb{R}^{24}$ and $\mathbb{R}^{25}$. In particular, weprove that maximum size of spherical three-distance sets is $2300$ in $\mathbbR^{23}$.

Semidefinite Programming Bounds For Spherical Three-distance Sets