Low Ambiguity Zone (LAZ) sequences play a pivotal role in modern integrated sensing and communication (ISAC) systems. Recently, Wang et al.[1] proposed a definition of locally perfect nonlinear functions (LPNFs) and constructed three classes of both periodic and aperiodic LAZ sequence sets with flexible parameters by applying such functions and interleaving method. Some of these LAZ sequence sets are asymptotically optimal with respect to the Ye-Zhou-Liu-Fan-Lei-Tang bounds undercertain conditions. In this paper, we proceed with the construction of LPNFs with new parameters. By using these LPNFs, we also present a series of LAZ sequence sets with more flexible parameters, addressing the limitations of existing parameter choices. Furthermore, our results show that one of these classes is asymptotically optimal in both the periodic and aperiodic cases, respectively.

翻译：低模糊区（LAZ）序列在现代集成感知与通信（ISAC）系统中发挥着关键作用。最近，Wang等人[1]提出了局部完美非线性函数（LPNFs）的定义，并利用此类函数与交织方法，构造了三类具有灵活参数的周期与非周期LAZ序列集。其中部分LAZ序列集在特定条件下关于Ye-Zhou-Liu-Fan-Lei-Tang界是渐近最优的。本文继续构造具有新参数的LPNFs。通过使用这些LPNFs，我们进一步提出了一系列参数选择更为灵活的LAZ序列集，从而解决了现有参数选择的局限性。此外，我们的结果表明，其中一类序列集分别在周期与非周期情形下均具有渐近最优性。