In 1987, Huw Davies proved that, for a flag-transitive point-imprimitive 2- $\left(v,k,\lambda \right)$ design, both the block-size $k$ and the number $v$ of points are bounded by functions of $\lambda$, but he did not make these bounds explicit. In this paper we derive explicit polynomial functions of $\lambda$ bounding $k$ and $v$. For $\lambda ⩽4$ we obtain a list of “numerically feasible” parameter sets $v,k,\lambda$ together with the number of parts and part-size of an invariant point-partition and the size of a nontrivial block-part intersection. Moreover from these parameter sets we determine all examples with fewer than 100 points. There are exactly 11 such examples, and for one of these designs, a flag-regular, point-imprimitive $2-\left(36,8,4\right)$ design with automorphism group ${\mathrm{S}}_6$, there seems to be no construction previously available in the literature.

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关于标志传递非原语 2-设计

1987 年，Huw Davies 证明了，对于一个标志传递的点非原语 2- $\left(v,克,\lambda \right)$ 设计，无论是块大小 $克$ 和数量 $v$ 点的边界由函数 $\lambda$，但他没有明确说明这些界限。在本文中，我们推导出显式多项式函数$\lambda$ 边界 $克$ 和 $v$. 为了$\lambda ⩽4$ 我们获得“数值可行”参数集列表 $v,克,\lambda$连同不变点分区的部分数量和部分大小以及非平凡块部分交集的大小。此外，根据这些参数集，我们可以确定所有少于 100 个点的示例。正好有 11 个这样的例子，对于其中一个设计，旗规则，点不规则$2-\left(36,8,4\right)$ 带自同构组的设计 ${\mathrm{秒}}_6$，以前文献中似乎没有可用的构造。