  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 FHSs
and FHS sets with optimal partial Hamming correlation. We first establish a
correspondence between FHS sets with optimal partial Hamming correlation and
multiple partition-type balanced nested cyclic difference packings with a
special property. By virtue of this correspondence, some FHSs and FHS sets with
optimal partial Hamming correlation are constructed from various combinatorial
structures such as cyclic difference packings, and cyclic relative difference
families. We also describe a direct construction and two recursive
constructions for FHS sets with optimal partial Hamming correlation. As a
consequence, our constructions yield new FHSs and FHS sets with optimal partial
Hamming correlation.
