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  "body": "\n## Summary\n\nA low-discrepancy sequence is a sequence of points in the unit cube $[0, 1)^s$ whose initial segments fill the cube as evenly as possible.\nEvenness is measured by the star discrepancy.\nIt compares the share of the first $N$ points in each box anchored at the origin with the volume of the box.\nFor a low-discrepancy sequence the largest difference is of order $(\\log N)^s / N$.\nFor large $N$ this is much smaller than the typical value of order $N^{-1/2}$ for random points.\nSuch sequences are the point sets of quasi-Monte Carlo integration.\nEvery low-discrepancy sequence is uniformly distributed in the cube; for $s = 1$ this is [[equidistribution modulo one|XM6DH57BWY]].\n\n## Explanations\n\n### L1 human\n\nRandom points tend to clump in some places and leave gaps in others.\nA low-discrepancy sequence places each new point in a region that is still empty, so that at every stage the points are spread out evenly.\nThe simplest example on $[0, 1)$ is the van der Corput sequence $\\frac12, \\frac14, \\frac34, \\frac18, \\frac58, \\frac38, \\frac78, \\ldots$, obtained by writing $1, 2, 3, \\ldots$ in binary and mirroring the digits at the binary point.\nIn higher dimension, the Halton and Sobol sequences play the same role.\nAverages of a function over such points approximate its integral with a smaller error than random points.\n",
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