On the Assessment of Random and Quasi-Random Point Sets

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The Monte Carlo and the quasi-Monte Carlo method are two of the most important techniques to solve multidimensional problems. In both cases, we employ deterministic algorithms to generate finite point sets in high dimensions. The quality of the equidistribution of these point sets may have a decisive influence on our numerical results. In this contribution, we will discuss the main concepts to assess equidistribution. In particular, we will present a new interpretation of the well-known spectral test.