Block design
From Groupprops
Definition
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.
Further definition
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.