Minimal Enclosings of Group Divisible Designs with Block Size 3 and Group Size 2

We obtain necessary conditions for the enclosing of a group divisible design with block size 3, \( \text{GDD}(n, m; \lambda) \), into a group divisible design \( \text{GDD}(\text{n}, \text{m+1}; \lambda+\text{x}) \) with one extra group and minimal increase in \( \lambda \). We prove that the necessary conditions are sufficient for the existence of all such enclosings for GDDs with group size 2 and \( \lambda \leq 6 \), and for any \( \lambda \) when \( v \) is sufficiently large relative to \( \lambda \).