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In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employing d -form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets using m -sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriate d -form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets.