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 $\mathrm{\text{SL}}(2,{\mathbb{F}}_q)$. Until now the only known infinite families 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.

如果连贯性尽可能小，则行打包是最佳的。最佳线包装的最有趣的例子是在一些已知的连贯性下限中实现相等。在本文中，提出了两个无限系列的实数和复数双角线包装。新包装分别在实数或复数第二个 Levenshtein 界中实现相等。两个无限族都是通过分析有限群的众所周知的表示来构建的$\mathrm{\text{SL}}(2,{\mathbb{F}}_q)$. 到目前为止，唯一已知的满足第二个 Levenshtein 界限的无限族与最大互无偏基集 (MUB) 有关。与与最大 MUB 集相关的行封装类似，这里介绍的行封装与相互无偏的称重矩阵的最大集相关。另一个相似之处是新填料是射影 2 设计。后一种性质与新填料足够大的基数一起意味着对真实和复杂双角紧框架的最大已知基数的一些改进。