Abstract: We extended the nuclear design of  combinatorial design theory, and considered a more general  group divisible nuclear design. By using the method of direct construction and recursive construction, we  solved the existence problem of the group divisible nuclear design with block K₄-e and equal size group,  and proved that there existed a group divisible (K₄-e)nuclear design of type gⁿ for n≥3, g≥1.

Key words: group divisible design, nuclear design, graph packing, graph covering