  Frequency hopping sequences (FHSs) are employed to mitigate the interferences
caused by the hits of frequencies in frequency hopping spread spectrum systems.
In this paper, we present some new algebraic and combinatorial constructions
for FHS sets, including an algebraic construction via the linear mapping, two
direct constructions by using cyclotomic classes and recursive constructions
based on cyclic difference matrices. By these constructions, a number of series
of new FHS sets are then produced. These FHS sets are optimal with respect to
the Peng-Fan bounds.
