Geodesic
Constructing block designs of elements or residue rings with a composite modulus
Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 649-658.

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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. 
@article{MZM_1971_10_6_a6,
     author = {B. T. Rumov},
     title = {Constructing block designs of elements or residue rings with a composite modulus},
     journal = {Matemati\v{c}eskie zametki},
     pages = {649--658},
     publisher = {mathdoc},
     volume = {10},
     number = {6},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a6/}
}
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B. T. Rumov. Constructing block designs of elements or residue rings with a composite modulus. Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 649-658. http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a6/