Definition with symbols
A -block design is the following data:
- A set with elements, called the vertices
- A collection of -element subsets of , called blocks. The number of blocks is denoted as
Satisfying the following conditions:
- Every point is contained in the same number of blocks (this is denoted as )
- Given any two points, the number of blocks containing both of them is
This is also called a BIBD or a Balanced Incomplete Block Design.
A generalization of block design is to -block design. A -block design has the property that for any elements, the number of blocks cotaining all of them is fixed and independent of the choice of elements. Such a thing is called, in more detail, a block design.