  Frequency hopping sequences (FHSs) with favorable partial Hamming correlation
properties have important applications in many synchronization and
multiple-access systems. In this paper, we investigate constructions of FHS
sets with optimal partial Hamming correlation. We present several direct
constructions for balanced nested cyclic difference packings (BNCDPs) and
balanced nested cyclic relative difference packings (BNCRDPs) such that both of
them have a special property by using trace functions and discrete logarithm.
We also show three recursive constructions for FHS sets with partial Hamming
correlation, which are based on cyclic difference matrices and discrete
logarithm. Combing these BNCDPs, BNCRDPs and three recursive constructions, we
obtain infinitely many new strictly optimal FHS sets with respect to the
Peng-Fan bounds.
