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  "body": "\n## Summary\n\nA blocking set in a [[projective plane|DANFNN8C4Y]] is a set of points that meets every line.\nAny line is a blocking set, so the interesting ones are those that contain no whole line.\nThe study of their smallest sizes is a main theme of finite geometry, with links to coding theory and to polynomials over finite fields.\n\n## Explanations\n\n### L1 human\n\nImagine guards placed on points of a finite plane, with the rule that every line must contain a guard.\nPutting all guards on one line works, but it is boring.\nA blocking set that contains no complete line must be spread out, and it needs more points than a line.\nIn a plane of order $n$ it needs at least $n + \\sqrt{n} + 1$ points.\nWhen $n$ is a square, a smaller copy of a plane of order $\\sqrt{n}$ inside the plane reaches this bound.\n",
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