An Improved Inequality for Balanced Incomplete Block Designs
The Annals of Mathematical Statistics, 1971 For a resolvable balanced incomplete block design (BIBD), Bose (1942) obtained an inequality $b \geqq v + r - 1$. Stanton (1957) showed that this inequality is equivalent to an inequality $r \geqq \lambda + k$. The main purpose of this note is to improve Bose's inequality to $b \geqq 2\nu + r - 2$ for a resolvable BIBD which is not affine resolvable.
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Improved inequalities for balanced incomplete block designs
Discrete Mathematics, 1978 AbstractIt is known that there are some lower bounds for the number of blocks in a balanced incomplete block design (BIBD). Especially, Fisher's inequality b⩾v is well-known for a BIBD with parameters v, b, r, k and λ. Fisher's inequality can be improved upon if one puts additional restrictions on a BIBD.
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A Balanced Incomplete Block Design
The Annals of Mathematical Statistics, 1965 openaire +3 more sources
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