Abstract
A theorem is proved that every resolvable BIB-design (v,k,λ) with λ=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,λ) with λ=k−1 and λ=(k−1)/2.
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Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 707–715, May, 1977.
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Rumov, B.T. A recursive method of construction of resolvable BIB-designs. Mathematical Notes of the Academy of Sciences of the USSR 21, 395–399 (1977). https://doi.org/10.1007/BF01788237
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DOI: https://doi.org/10.1007/BF01788237