Set Size Bound for Aperiodic Z-Complementary Code Sets

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