  In literatures, there are various constructions of frequency hopping sequence
(FHS for short) sets with good Hamming correlations. Some papers employed only
multiplicative groups of finite fields to construct FHS sets, while other
papers implicitly used only additive groups of finite fields for construction
of FHS sets. In this paper, we make use of both multiplicative and additive
groups of finite fields simultaneously to present a construction of optimal FHS
sets. The construction provides a new family of optimal
$\left(q^m-1,\frac{q^{m-t}-1}{r},rq^t;\frac{q^{m-t}-1}{r}+1\right)$ frequency
hopping sequence sets archiving the Peng-Fan bound. Thus, the FHS sets
constructed in literatures using either multiplicative groups or additive
groups of finite fields are all included in our family. In addition, some other
FHS sets can be obtained via the well-known recursive constructions through
one-coincidence sequence set.
