We determine a necessary and sufficient condition for the existence of semicyclic holey group divisible designs with block size three and group type $\left(n,m^t\right)$. New recursive constructions on semicyclic incomplete holey group divisible designs are introduced to settle this problem completely.

中文翻译：

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块大小为3的半环状多孔群可分设计的频谱

我们确定存在块大小为三，组类型为半圆孔的可分组整除设计的必要和充分条件 $（ñ，{米}^{Ť}）$。引入了半循环不完全孔组可分割设计上的新递归构造以完全解决该问题。