The widely and commonly adopted upper bound on the set size of aperiodic Z-complementary sets (ZCSs) in the literature has been a conjecture. In this letter, we provide detailed derivations for this conjectured bound. A ZCS is optimal when its set size reaches the upper bound. Furthermore, we propose a new construction of ZCSs based on extended generalized Boolean functions (EGBFs). The proposed method introduces optimal ZCSs with new parameters.

翻译：文献中广泛采用的非周期Z互补集合（ZCSs）集合规模上界一直是一个猜想。本文详细推导了这一猜想上界。当ZCS的集合规模达到该上界时，该集合即为最优ZCS。此外，我们提出了一种基于扩展广义布尔函数（EGBFs）的ZCS新构造方法。所提方法能够构造出具有新参数的最优ZCS。