Constructing block designs of elements or residue rings with a composite modulus

The paper provides a construction of cyclic BIB designs with parameters $b, v, r, k$, and $\lambda$ such that $\lambda=k-1$, $k\geqslant3$, and $p\equiv1\pmod{k}$ for each prime divisor $p$ of the number $v$. The existence is proven of bases consisting of $(v-1)/k$ blocks and, for $v=p^\alpha$, this base is given explicitly.