基于对称和仿射区组设计及互无偏基的最优扩展子空间填充的构造和性质
Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases
摘要：
我们继续研究的最佳弦包装，重点包装子空间的尺寸大于一。遵循在以前的工作中概述的原则，作者使用最大仿射区组设计和最大集的相互无偏的基础上构建格拉斯曼$2$ -设计，我们表明，他们的方法扩展到其他类型的区组设计，导致过多的最佳子空间包装的特点是由orthoplex界。更一般地说，我们表明，任何最佳弦包装必然是一个融合框架，其空间补充也是最佳的。
英文摘要：
We continue the study of optimal chordal packings, with emphasis on packing subspaces of dimension greater than one. Following a principle outlined in a previous work, where the authors use maximal affine block designs and maximal sets of mutually unbiased bases to construct Grassmannian $2$-designs, we show that their method extends to other types of block designs, leading to a plethora of optimal subspace packings characterized by the orthoplex bound. More generally, we show that any optimal chordal packing is necessarily a fusion frame and that its spatial complement is also optimal.
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