---
tag: 4JCSS2Z1BA
kind: concept
name: Block design
msc: [05B05]
specializes: [PAJTMQ604P]
sources:
  - url: https://en.wikipedia.org/wiki/Block_design
same_as:
  wikidata: Q751484
  wikipedia: Block design
---

## Summary

A block design is a finite set of points together with a family of subsets of the same size, the blocks.
It is balanced: every set of $t$ points lies in the same number of blocks.
The most studied case is $t = 2$, the balanced incomplete block design.
Block designs are a central kind of [[combinatorial design|PAJTMQ604P]].
They appear in the planning of experiments, in finite geometry and in coding theory.
The node [[block design|TGZATGBHTH]] gives the precise definition.

## Explanations

### L1 human

Think of a tournament organiser who must split players into groups of the same size so that every two players meet equally often.
The players are the points and the groups are the blocks.
A small example uses $7$ points and $7$ blocks of size $3$, in which every two points share exactly one block.
This example is the [[Fano plane|QQ8GW1ASZM]].