Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In 2006, Ge, Fuji-Hara and Miao constructed optimal FHSs with parameters \( (\frac{q^{w+1}-1}{q-1}, \frac{q^{w-1}-1}{q-1}+1, q^2-1) \) and \( (\frac{q^{2w+2}-1}{q-1}, \frac{q^{w+1}-1}{q-1}, q^{w+1}+1) \) achieving the Lempel-Greenberger bound based on projective geometries, where q is a prime power. Inspired by their work, we present four new constructions for FHSs, including three direct constructions based on projective geometries and one extension construction using units of rings and projective geometries. Utilizing these constructions, we have obtained four new series of optimal FHSs and a new family of nearly optimal FHSs.
