Novák conjectured in 1974 that for any cyclic Steiner triple systems of order v with $v\equiv 1(\mathrm{mod}6)$, it is always possible to choose one block from each block orbit so that the chosen blocks are pairwise disjoint. We consider the generalization of this conjecture to cyclic $(v,k,\lambda )$-designs with $1⩽\lambda ⩽k-1$. Superimposing multiple copies of a cyclic symmetric design shows that the generalization cannot hold for all v, but we conjecture that it holds whenever v is sufficiently large compared to k. We confirm that the generalization of the conjecture holds when v is prime and $\lambda =1$ and also when $\lambda ⩽(k-1)/2$ and v is sufficiently large compared to k. As a corollary, we show that for any $k⩾3$, with the possible exception of finitely many composite orders v, every cyclic $(v,k,1)$-design without short orbits is generated by a $(v,k,1)$-disjoint difference family.

在1974年诺瓦克推测，订单的任何循环斯坦纳三元系v带$v\equiv 1(\mathrm{模组}6)$，总是可以从每个块轨道中选择一个块，以便选择的块成对不相交。我们考虑将这个猜想推广到循环$(v,克,\lambda )$-设计与 $1⩽\lambda ⩽克-1$. 叠加循环对称设计的多个副本表明泛化不能适用于所有v，但我们推测只要v与k相比足够大，它就适用。我们确认当v是素数时，猜想的推广成立，并且$\lambda =1$ 还有什么时候 $\lambda ⩽(克-1)/2$并且v与k相比足够大。作为推论，我们证明对于任何$克⩾3$，除了有限多个复合阶数v 之外，每个循环$(v,克,1)$-没有短轨道的设计是由一个 $(v,克,1)$-不相交的差异家庭。