---
tag: ZD8FVT10D8
kind: concept
name: Blocking set
msc: ["51E21", 05B25]
sources:
  - url: https://en.wikipedia.org/wiki/Blocking_set
same_as:
  wikidata: Q17005980
  wikipedia: Blocking set
---

## Summary

A blocking set in a [[projective plane|DANFNN8C4Y]] is a set of points that meets every line.
Any line is a blocking set, so the interesting ones are those that contain no whole line.
The study of their smallest sizes is a main theme of finite geometry, with links to coding theory and to polynomials over finite fields.

## Explanations

### L1 human

Imagine guards placed on points of a finite plane, with the rule that every line must contain a guard.
Putting all guards on one line works, but it is boring.
A blocking set that contains no complete line must be spread out, and it needs more points than a line.
In a plane of order $n$ it needs at least $n + \sqrt{n} + 1$ points.
When $n$ is a square, a smaller copy of a plane of order $\sqrt{n}$ inside the plane reaches this bound.