考慮空間中過原點的若干條直線，若任兩條直線間所形成的夾角只有一種角度，我們稱該集合為等角直線叢。這樣的構造可以由空間中單位球面上的有限點集合（即球面碼）來描述。球面上的離散幾何極值問題有著相當悠久的歷史，知名的問題有吻球數問題、球面上最密堆積問題及能量最小化問題等。在這篇文章中，我們複習目前用來解以上問題的主流方法，即Delsarte的線性規劃及Bachoc-Vallentin的半正定規劃等最佳化方法，並考慮後者的對偶問題來重現歐式空間中維度介於$23$與$60$間且角度為acos(1/5)的等角直線叢的上界。;Equiangular lines is a set of lines through the origin in the space with a single angle between any two of them. It can be identified as a finite set of points on the sphere which is known as spherical code. The search for extreme structures of spherical codes satisfying certain conditions has a long history in discrete geometry, such as the kissing number problem, Tammes′ problem, and energy minimizing problem. In this paper, we review two effective methods for dealing with those long-standing questions, namely, Delsarte′s linear programming and Bachoc-Vallentin′s semidefinite programming, and use the dual form of the latter to reproduce the bound on equiangular lines of angle acos(1/5) in R^n where 22<n<61.
