We explore the space of matrix-generated (0, m, 2)-nets and (0, 2)-sequences in base 2, also known as digital dyadic nets and sequences. In computer graphics, they are arguably leading the competition for use in rendering. We provide a complete characterization of the design space and count the possible number of constructions with and without considering possible reorderings of the point set. Based on this analysis, we then show that every digital dyadic net can be reordered into a sequence, together with a corresponding algorithm. Finally, we present a novel family of self-similar digital dyadic sequences, to be named $\xi$-sequences, that spans a subspace with fewer degrees of freedom. Those $\xi$-sequences are extremely efficient to sample and compute, and we demonstrate their advantages over the classic Sobol (0, 2)-sequence.

翻译：我们探讨了基于矩阵生成的基2（0，m，2）-网和（0，2）-序列（亦称数字二进网与序列）的空间。在计算机图形学中，它们堪称渲染领域最具竞争力的选择。我们完整刻画了该设计空间的特性，并统计了考虑与不考虑点集重排序时的可能构造数量。基于此分析，我们进一步证明每个数字二进网均可通过相应算法重排为序列。最后，我们提出一类名为ξ-序列的新型自相似数字二进序列，其张成子空间具有更少的自由度。这些ξ-序列在采样与计算中极为高效，我们展示了它们相较于经典Sobol (0,2)-序列的优越性。