Digital nets (in base $2$) are the subsets of $[0,1]^d$ that contain the expected number of points in every not-too-small dyadic box. We construct sets that contain almost the expected number of points in every such box, but which are exponentially smaller than the digital nets. We also establish a lower bound on the size of such almost nets.
翻译:数字网(基数为$2美元)是$[0,1]d$的子集,它包含每个非小数字箱的预期点数。我们建造的数组几乎包含每个这类箱的预期点数,但比数字网的指数小。我们还对几乎这样一个网的大小定了一个较低的界限。