AI 中文总结
探索双角线与整数格联系，对维度7到10中特定角度的最大双角线系统分类，给出维度15中规模与已知最大匹配的新双角线系统，利用双角线与整数格联系构建并分类双角线系统。
AI 中文摘要
维度7到20中已知最大的双角线系统由Ganzhinov和Szöllősi给出，其线夹角为arccos(1/5)和arccos(1/5)，利用与整数格的良好联系构建。本文进一步探索双角线与整数格的联系，对维度7到10中具有这些角度的最大双角线系统进行分类，还给出了维度15中的一个新双角线系统，其规模与该维度已知最大的匹配。
英文摘要
The largest known biangular lines systems in dimension 7 through 20 are due to Ganzhinov and Szöllősi, and the lines make angles $\arccos(\frac{1}{5})$ and $\arccos(\frac{3}{5})$. They are constructed by making use of the nice connection with integral lattices. We explore further the connection between biangular lines and integral lattices to classify the largest biangular line systems with these angles, in dimension 7 through 10. We also give a new biangular line system in dimension 15, that matches the size of the largest known in this dimension.
Comments32 pages
