DifferenceFamily

Let $\mathcal B=\{B_i\}$ be a collection of subsets of a group $G$ of order $v$ such that all $B_i$ are of order $k$. Let $\lambda(a)=\{(b,c,i)\mid b,c\in B_i$, $b-c=a\}$. If there exists an interger $\lambda$ such that $|\lambda(a)|=\lambda$ for all $a\in G$, then we call $\mathcal B$ a $(v,k,\lambda)$ difference family.