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arXiv · 0809.2282

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

Muhammad Ali Khan
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Abstract

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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Muhammad Ali Khan. 2015-05-31. New lower bounds for the number of blocks in balanced incomplete block designs. https://arxiv.org/abs/0809.2282

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