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  "body": "\n## Summary\n\nIn 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, ... .\n",
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