We introduce a new quality measure to assess randomized low-discrepancy point sets of finite size $n$. This new quality measure, which we call "pairwise sampling dependence index", is based on the concept of negative dependence. A negative value for this index implies that the corresponding point set integrates the indicator function of any unanchored box with smaller variance than the Monte Carlo method. We show that scrambled $(0,m,s)-$nets have a negative pairwise sampling dependence index. We also illustrate through an example that randomizing via a digital shift instead of scrambling may yield a positive pairwise sampling dependence index.

翻译：我们引入了新的质量衡量标准, 评估随机的低差异点数, 范围有限, 单位为$。 这个新的质量衡量标准, 我们称之为“ 偏差抽样依赖指数 ”, 以负依赖性概念为基础。 这个指数的负值意味着相应的点数将任何未分解的框的指标功能整合起来, 其差异小于蒙特卡洛方法。 我们显示, 折合的 $( 0. m, s)- $ net 具有负对比抽样依赖性指数。 我们还通过一个例子来说明, 通过数字转换而不是拼拼凑随机, 可能会产生正对比的抽样依赖性指数 。