Abstract: In frequency hopping communication system, frequency hopping sequences have a decisive influence on the entire frequency hopping communication system. Constructing a set of frequency hopping sequences that meet the requirements of the theoretical bound is the key content of researching frequency hopping communication systems. The average Hamming correlation is used to measure the average error of the frequency hopping communication system. In this paper, we first choose a basis sequence based on cyclotomy and then a set of frequency hopping sequences is constructed based on cyclotomy and the Chinese remainder theorem in the finite field. The results show that the proposed set with more flexible parameters is optimal with respect to the average Hamming correlation.