Divisible difference set for a subgroup

Definition
Let $$G$$ be a finite group of order $$mn$$ and $$N$$ be a subgroup of $$G$$ of order $$m$$. Then we say that a subset $$D$$ of $$G$$ is a divisible difference set with exceptional subgroup $$N$$ if there are constants $$\lambda_1$$ and $$\lambda_2$$ such that:


 * Every non-identity element of $$N$$ can be expressed as a right quotient of elements in $$D$$ in exactly $$\lambda_1$$ ways.
 * Every element in $$G \setminus N$$ can be expressed as a right quotient of elements in $$D$$ in exactly $$\lambda_2$$ ways.