An Inequality for Balanced Incomplete Block Designs

Abstract

For a resolvable balanced incomplete block design, R. C. Bose [1] obtained the inequality $b \geqq v + r - 1$, and P. M. Roy [2] and W. F. Mikhail [3] proved this inequality without the assumption of resolvability, but with the weaker assumption that $v$ is a multiple of $k$. In this note an alternative and simpler proof of Roy's theorem is given.