论文标题
与$ \ textrm {sl}的表示相关的双线线的最佳系统的无限族（2，\ mathbb {f} _q）$
Infinite families of optimal systems of biangular lines related to representations of $\textrm{SL}(2,\mathbb{F}_q)$
论文作者
论文摘要
如果线条尽可能小，则管线堆积是最佳的。最佳线条包装的最有趣的例子是在某些已知的下限中实现平等，以达到连贯性。在本文中，提出了两个无限和复杂的双线线包装的家族。新包装分别在实际或复杂的第二Levenshtein结合中达到平等。这两个无限族都是通过分析有限组SL $（2，\ Mathbb {f} _Q）$的众所周知的表示来构建的。到目前为止，唯一已知的无限家族符合第二列文申的界限与互无偏基（MUB）的最大群体相关。与与最大MUB相关的线包装类似，此处介绍的线包装与相互无偏的称重矩阵的最大组合有关。另一个相似之处是，新包装是投影2设计。后一种特性以及新包装的足够大的红衣主教意味着对最大和复杂的双重双重紧密框架的最大红衣主教有所改善。
A line packing is optimal if its coherence is as small as possible. Most interesting examples of optimal line packings are achieving equality in some of the known lower bounds for coherence. In this paper two infinite families of real and complex biangular line packings are presented. New packings achieve equality in the real or complex second Levenshtein bound respectively. Both infinite families are constructed by analyzing well known representations of the finite groups SL$(2,\mathbb{F}_q)$. Until now the only known infinite familes meeting the second Levenshtein bounds were related to the maximal sets of mutually unbiased bases (MUB). Similarly to the line packings related to the maximal sets of MUBs, the line packings presented here are related to the maximal sets of mutually unbiased weighing matrices. Another similarity is that the new packings are projective 2-designs. The latter property together with sufficiently large cardinalities of the new packings implies some improvement on largest known cardinalities of real and complex biangular tight frames.
