Definition:Balanced Incomplete Block Design

A Balanced Incomplete Block Design or BIBD with parameters $$v, b, r, k, \lambda$$ is a block design where:
 * $$v$$ 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 $$ { v \choose 2 }$$ pairs occur together in exactly $$\lambda$$ blocks.

A BIBD with parameters $$v, b, r, k, \lambda$$ is commonly written several ways:
 * BIBD$$(v,k,\lambda)$$
 * $$(v,k,\lambda)$$-BIBD

Properties
For any BIBD $$(v,k,\lambda)$$ the following are true: Note: All of the above are integers.
 * $$bk=rv$$
 * $$\lambda(v-1) = r(k-1)$$
 * $$b=\frac\lambda=\frac{v(v-1)\lambda}{k(k-1)}$$
 * $$b\geq{v}$$ This is known as Fisher's Inequality.