## Related pagesSymmetric designsSteiner systems |

Given a set with v elements and a number , we may choose all k element subsets of as our blocks. This structure is a design for all with

These designs are called the trivial designs. Each design is also a design for each with

In particular, the number of lines is exactly

Some types of designs have special names, for example

- The designs are exactly the, eventually degenerate, finite projective planes.
- The designs are exactly the, eventually degenerate, finite affine planes.
- The designs with v>0 are exactly the Steiner triple systems.

Version