---
tag: B7SKJ1GP5P
kind: concept
name: Cap set
aliases: [exponential-bound-on-capsets]
sources:
  - wikipedia: en:51223601@r1367780306
    locator: Cap set
    note: adopted
    mention: wikipedia://en/51223601
    sections: [Summary]
same_as:
  wikidata: Q28455422
  wikipedia: Cap set
inventory: [4NMBYD43W1]
---

## Summary

In affine geometry, a **cap set** is a subset of the affine space $\mathbb{Z}_3^n$ (the $n$-dimensional [[affine space|09XNAPTJQ7]] over the [[three-element field|0ZXZ82FTX2]]) where no three elements sum to the zero vector. The **cap set problem** is the problem of finding the size of the largest possible cap set, as a function of $n$. The first few cap set sizes are 1, 2, 4, 9, 20, 45, 112, ... .