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The research of cyclotomy theory can be traced to Gauss and it has been applied to many fields such as cryptography, coding theory, and combinatorics. According to <inline-formula> <tex-math notation="LaTeX">$v$ </tex-math></inline-formula> prime numbers or compound words, the incision on the residue-like ring <inline-formula> <tex-math notation="LaTeX">${\mathbb Z}_{v}$ </tex-math></inline-formula> can be separated to classic incision or general incision. In this work, a kind of extended generalized cyclotomic classes is introduced. Based on this tangent method, a class of frequency hopping sequence set with the best average Hamming correlation is proposed.