NHZ frequency hopping sequence sets under aperiodic Hamming correlation: Tighter bound and optimal constructions

In this paper, we first establish a new bound on no-hit-zone (NHZ) frequency hopping (FH) sequence sets under aperiodic Hamming correlation. The new bound is tighter than the bound on NHZ FH sequence sets under aperiodic Hamming correlation which was derived by Liu et al. (Electron. Lett. 54, 212–213, 2018). Then we construct a class of NHZ FH sequence sets under aperiodic Hamming correlation. They are optimal with respect to the new bound and have more flexible parameters than those in Liu et al. (Electron. Lett. 54, 212–213, 2018). Further, we give a construction of NHZ FH sequence sets with low aperiodic Hamming correlation value outside of NHZ which are also optimal with respect to the new bound.