Low ambiguity zone (LAZ) sequences play a crucial role in modern integrated sensing and communication (ISAC) systems. In this paper, we introduce a novel class of functions known as locally perfect nonlinear functions (LPNFs). By utilizing LPNFs and interleaving techniques, we propose three new classes of both periodic and aperiodic LAZ sequence sets with flexible parameters. The proposed periodic LAZ sequence sets are asymptotically optimal in relation to the periodic Ye-Zhou-Liu-Fan-Lei-Tang bound. Notably, the aperiodic LAZ sequence sets also asymptotically satisfy the aperiodic Ye-Zhou-Liu-Fan-Lei-Tang bound, marking the first construction in the literature. Finally, we demonstrate that the proposed sequence sets are cyclically distinct.

翻译：低模糊区序列在现代一体化感知与通信系统中发挥着至关重要的作用。本文引入了一类称为局部完美非线性函数的新函数。通过利用局部完美非线性函数与交织技术，我们提出了三类具有灵活参数的非周期与周期低模糊区序列集。所提出的周期低模糊区序列集在渐近意义上相对于周期 Ye-Zhou-Liu-Fan-Lei-Tang 界是最优的。值得注意的是，所提出的非周期低模糊区序列集也渐近满足非周期 Ye-Zhou-Liu-Fan-Lei-Tang 界，这是文献中的首次构造。最后，我们证明了所提出的序列集是循环互异的。