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.