New lower bounds for the number of blocks in balanced incomplete block designs

Details New lower bounds for the number of blocks in balanced incomplete block designs New lower bounds for the number of blocks in balanced incomplete block designs

2008-09-12

arxiv.org/abs/0809.2282v1

Mathematics

Combinatorics

7 pages

Scientific paper

Bose proved the inequality $b\geq v+r-1$ for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note we prove a new lower bound on the number of blocks $b$ that holds for all BIBDs. We further prove that for a significantly large number of BIBDs our bound is tighter than the bounds given by the inequalities of Bose and Kageyama.

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