\begin{definition}[Definition:Balanced Incomplete Block Design]
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 points in the design
:$b$ is the number of blocks
:$k$ is the size of each block
:$r$ is the number of blocks any point can be in
:$\lambda$ is the number of times any two points 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:
:$\map {\operatorname {BIBD} } {v, k, \lambda}$
:$\tuple {v, k, \lambda}$-$\operatorname{BIBD}$
\end{definition}