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  "body": "\n## Summary\n\nA Steiner system $S(t, k, n)$ is a set of $n$ points with a family of $k$-element blocks.\nEvery $t$ points lie in exactly one block.\nIt is a [[block design|4JCSS2Z1BA]] with $\\lambda = 1$.\nSteiner triple systems, finite projective planes and the large Witt design $S(5, 8, 24)$ are the best-known examples.\nThe node [[Steiner system|QHPW53E7YA]] gives the precise definition.\n\n## Explanations\n\n### L1 human\n\nA Steiner system is a way to group points into blocks of equal size so that any choice of $t$ points determines exactly one block.\nWith $t = 2$, two points always lie together in exactly one block, like two points on exactly one line.\nThe [[Fano plane|QQ8GW1ASZM]] is a Steiner system $S(2, 3, 7)$: $7$ points, $7$ blocks of size $3$, and every pair of points in one block.\n",
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