Minimum Redundancy Linear Arrays (MRLAs) are special linear arrays that provide the narrowest main lobe in the radiation pattern possible for a given number of antennas. We found that the calculation of MRLAs is the same as for the mathematical problem of perfect sparse rulers. Finding perfect rulers (or MRLAs) is a hard problem, as there is no proven mathematical rule to design them. They can only be found by constructing ruler candidates via an exhaustive search while ensuring that no ruler with less redundancy exists. We revisited the problem of sparse ruler construction and used two exhaustive search algorithms to compute longer rulers than previously published. Further, we present an approach to accelerate the execution by distributing the recursive search algorithms over multiple computers. Our compute cluster found perfect rulers with all lengths up to 244 in 443 years of combined CPU time. All found rulers are provided to the research community. Additionally, we confirm previously known Low Redundancy Linear Arrays being MRLAs. Our results show that larger perfect rulers do not always require equal or more marks (antennas) but can sometimes be constructed with fewer marks than the previous ruler.

中文翻译：

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大的最小冗余线性阵列：利用平行处理的完美和最优标尺的系统搜索

最小冗余线性阵列（MRLA）是特殊的线性阵列，可为给定数量的天线提供辐射方向图上最窄的主瓣。我们发现，MRLA的计算与完美稀疏标尺的数学问题相同。寻找完美的标尺（或MRLA）是一个难题，因为没有经过验证的数学规则可以设计它们。只有通过穷举搜索构造标尺候选者，同时确保不存在冗余度较小的标尺，才能找到它们。我们重新研究了稀疏标尺构造的问题，并使用了两种详尽的搜索算法来计算比以前发布的标尺更长的标尺。此外，我们提出了一种通过在多个计算机上分布递归搜索算法来加快执行速度的方法。我们的计算集群在443年的总CPU时间中发现了长度达244个的完美标尺。所有找到的统治者都提供给研究社区。此外，我们确认以前已知的低冗余线性阵列是MRLA。我们的结果表明，较大的完美标尺并不总是需要相等或更多的标记（天线），但有时可以用比以前的标尺更少的标记来构造。