球面三距離集合(spherical three-distance set)是指一個有限的單位向量集合，使得該集合滿足兩兩相異向量間的距離只有三種(也就是只有三種內積值)。最大基數的球面三距離集合是球面編碼理論裡的一個經典問題。
在此本篇論文，我們使用了半正定規劃方法，在許多維度中得到了更緊的上界。在7維，我們將上界從91降低到84；在23維，我們把上界從2301降低到2300，並且證明2300個點是最大基數的球面三距離集合在23維中。

A spherical three-distance set is a finite collection X of unit vectors in R^n such that for each pair of distinct vectors has three inner product values. The maximum cardinality of spherical three-distance set is a classic problem in spherical coding
theorem.
In this thesis, we use the semidefinite programming method to improve the upper bounds of spherical three-distance sets for several dimensions. We improve the upper bounds for spherical three-distance sets in R^7 from 91 to 84 and we prove that maximum size of spherical three-distance sets is 2300 in R^23.

1 Introduction 1
2 Previous method 4
3 Semidenite programming method 8
4 Discrete sampling points with Nozaki theorem 11
5 Continuous interval with sum of squares method 14
6 Experiments 19
7 Discussion and conclusion 29
Bibliography 31
A Uniform distribution on spherical space 34
B Correction on related paper 36

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