  Nov\'{a}k conjectured in 1974 that for any cyclic Steiner triple systems of
order $v$ with $v\equiv 1\pmod{6}$, 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 $1 \leq \lambda \leq k-1$. 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 $\lambda \leq (k-1)/2$ and $v$
is sufficiently large compared to $k$. As a corollary, we show that for any $k
\geq 3$, 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.
