In a paper published in 2005, Praeger and Zhou improved the upper bound on the number of points of a flag-transitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. Here we present an improvement of their result, devise a list of feasible parameter sequences for which two points are contained in at most ten blocks, and also develop new methods for the elimination of all but two such sequences. We used those methods to list all designs with given properties, with the exclusion of designs with said two sets of parameters for which we give limitations for their group of automorphisms.

中文翻译：

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具有 λ ≤ 10 的标志传递和点不原始对称设计

在 2005 年发表的一篇论文中，Praeger 和 Zhou 在包含两个点的块数方面改进了标志传递、点不原始、对称设计的点数上限。在这里，我们提出了他们的结果的改进，设计了一个可行参数序列列表，其中两个点包含在最多十个块中，并且还开发了新方法来消除除两个这样的序列之外的所有序列。我们使用这些方法列出了所有具有给定属性的设计，排除了具有上述两组参数的设计，我们为其自同构组提供了限制。