Group divisible designs (GDDs) with block size 4 and at most 30 points are known for all feasible group types except three, namely $2^3{5}^4,3^5{6}^2$, and $2^2{5}^5$. In this paper we provide solutions for the first two of these three 4‐GDDs without assuming any automorphisms. We also construct several other 4‐GDDs. These include classes of 4‐GDDs of types ${\left(3m\right)}^4{\left(6m\right)}^q{\left(3n\right)}^1$ for $0\le n\le \left(q+1\right)m$ where $q\in \left\{2,3\right\}$ and solutions for 4‐GDDs of types $3^t{6}^s$ for a wide range of values of $s\ge 2,t\ge 4$ satisfying $t\equiv 0$ or $1\left(\mathrm{mod}4\right)$, including all cases with $4\le t\le s-1$. Most of the remaining unknown 4‐GDDs of type $3^t{6}^s$ have $\left(s-1\right)<t<2\left(s-1\right)$.

中文翻译：

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一些具有块大小4和两个或三个组大小的新的组可分割设计

已知除3个块外的所有可行组类型的块大小为4且最多30个点的组可分割设计（GDD） $2^3{5}^4，3^5{6}^2$和 $2^2{5}^5$。在本文中，我们为这三个4-GDD中的前两个提供了解决方案，而没有假定任何同构。我们还构建了其他几个4-GDD。其中包括类型为4的GDD${（3米）}^4{（6米）}^q{（3ñ）}^{\mathrm{1个}}$ 对于 $0\le ñ\le （q+\mathrm{1个}）米$ 哪里 $q\in \left\{2，3\right\}$ 和类型的4‐GDD解决方案 $3^{Ť}{6}^s$ 适用于 $s\ge 2，Ť\ge 4$ 满意的 $Ť\equiv 0$ 要么 $\mathrm{1个}（\mathrm{模}4）$，包括所有与 $4\le Ť\le s-\mathrm{1个}$。其余大多数类型的未知4‐GDD$3^{Ť}{6}^s$ 有 $（s-\mathrm{1个}）<Ť<2（s-\mathrm{1个}）$。