Necessary conditions for the existence of a decomposable super‐simple resolvable $\left(v,4,6\right)$‐BIBD whose two component subdesigns are both resolvable $\left(v,4,3\right)$‐BIBDs are $v\equiv 0$ (mod $4$) and $v\ge 16$. In this paper, it is proved that these necessary conditions are sufficient, except possibly for $v\in \left\{268,284,292,296\right\}$.

中文翻译：

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具有块大小4和索引6的可分解超简单RBIBD

可分解的超简单可解的存在的必要条件 $（v，4，6）$‐BIBD的两个子组件设计均可解决 $（v，4，3）$‐BIBD是 $v\equiv 0$ （修改 $4$）和 $v\ge 16$。本文证明了这些必要条件是足够的，除了可能$v\in \left\{268，284，292，296\right\}$。