A subset $D=\{a_1,\ldots,a_k\}$ of $\mathbb{Z}/v\mathbb{Z}$ is said to be a $(v,k,\lambda)$-cycic difference set if for each nonzero $b\in\mathbb{Z}/v\mathbb{Z}$, there are exactly $\lambda$ ordered pairs $(a_s,a_t)\in D^2$ such that $a_s-a_t=b$. For a $(v,k,\lambda)$-difference set $D$, $k-\lambda$ is called the order of $D$.
Let $N_v$ be the number of different (even they are equivalent, different subsets of $\mathbb{Z}/v\mathbb{Z}$ viewd as different) cyclic difference sets in $\mathbb{Z}/v\mathbb{Z}$, and $N_{v,n}$ be the number of different $(v,k,\lambda)$-cyclic difference sets of order $n$. Are there any nontrivial upper bounds known for $N_v$ or $N_{v,n}$?
