The design of uniformly spread sequences on $[0,1)$ has been extensively studied since the work of Weyl and van der Corput in the early $20^{\text{th}}$ century. The current best sequences are based on the Kronecker sequence with golden ratio and a permutation of the van der Corput sequence by Ostromoukhov. Despite extensive efforts, it is still unclear if it is possible to improve these constructions further. We show, using numerical experiments, that a radically different approach introduced by Kritzinger in seems to perform better than the existing methods. In particular, this construction is based on a \emph{greedy} approach, and yet outperforms very delicate number-theoretic constructions. Furthermore, we are also able to provide the first numerical results in dimensions 2 and 3, and show that the sequence remains highly regular in this new setting.

翻译：自Weyl和van der Corput在20世纪初的开创性工作以来，在区间$[0,1)$上设计均匀分布序列的问题已被广泛研究。当前最优序列基于黄金分割Kronecker序列和Ostromoukhov提出的van der Corput序列置换。尽管已有大量研究，这些构造是否还能进一步改进仍不明确。我们通过数值实验证明，Kritzinger引入的一种根本不同的方法似乎优于现有方法。特别地，该构造基于一种贪心策略，却超越了非常精妙的数论构造。此外，我们首次提供了二维和三维的数值结果，并证明该序列在新维度下仍保持高度规律性。