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  "body": "\n## Summary\n\nA block design is a finite set of points together with a family of subsets of the same size, the blocks.\nIt is balanced: every set of $t$ points lies in the same number of blocks.\nThe most studied case is $t = 2$, the balanced incomplete block design.\nBlock designs are a central kind of [[combinatorial design|PAJTMQ604P]].\nThey appear in the planning of experiments, in finite geometry and in coding theory.\nThe node [[block design|TGZATGBHTH]] gives the precise definition.\n\n## Explanations\n\n### L1 human\n\nThink of a tournament organiser who must split players into groups of the same size so that every two players meet equally often.\nThe players are the points and the groups are the blocks.\nA small example uses $7$ points and $7$ blocks of size $3$, in which every two points share exactly one block.\nThis example is the [[Fano plane|QQ8GW1ASZM]].\n",
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