A recursive method of construction of resolvable $BIB$-designs
Matematičeskie zametki, Tome 21 (1977) no. 5, pp. 707-715
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A theorem is proved that every resolvable $BIB$-design $(v,k,\lambda)$ with $\lambda=k-1$ and the parameters $v$ and $k$ such that there exists a set of $k-1$ pairwise orthogonal Latin squares of order $v$ can be embedded in a resolvable $BIB$-design $(k+1)v,k,k-1)$. An analogous theorem is established for the class of arbitrary $BIB$-designs. As a consequence is deduced the existence of resolvable $BIB$-designs $(v,k,\lambda)$ with $\lambda=k-1$ and $(v,k,\lambda)$ with $\lambda=(k-1)/2$
@article{MZM_1977_21_5_a11,
author = {B. T. Rumov},
title = {A~recursive method of construction of resolvable $BIB$-designs},
journal = {Matemati\v{c}eskie zametki},
pages = {707--715},
year = {1977},
volume = {21},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_5_a11/}
}
B. T. Rumov. A recursive method of construction of resolvable $BIB$-designs. Matematičeskie zametki, Tome 21 (1977) no. 5, pp. 707-715. http://geodesic.mathdoc.fr/item/MZM_1977_21_5_a11/