Category:Balanced Incomplete Block Designs

This category contains results about Balanced Incomplete Block Designs.
Definitions specific to this category can be found in Definitions/Balanced Incomplete Block Designs.

A balanced incomplete block design or BIBD with parameters $v, b, r, k, \lambda$ is a block design such that:

$v$ is the number of treatments

$b$ is the number of blocks

$k$ is the size of each block

$r$ is the number of blocks any treatment can be in

$\lambda$ is the number of times any two treatments can occur in the same block

and has the following properties:

Each block is of size $k$

All of the $\dbinom v 2$ pairs occur together in exactly $\lambda$ blocks.

A BIBD with parameters $v, b, r, k, \lambda$ is commonly written several ways, for example:

$\map {\operatorname {BIBD} } {v, k, \lambda}$

$\tuple {v, k, \lambda}$-$\operatorname{BIBD}$