The existence of balanced ( υ , {3,6}, 1) difference families

Optimal frequency-hopping sequences can be constructed from cyclic ( υ, K , 1)-PBDs. A ( υ, K , 1) difference family can be used to construct a ( υ, K , 1)-PBD. A lot of work has been done on the existence of ( υ, k , 1) difference families when K = { k } is a singleton. For K = {3, 4}, it is proved that for each prime power υ ≡ 1 (mod 18) and υ ⩾ 19, there exists a balanced ( υ, K , 1) difference family. In this paper, it is proved that there exists a balanced ( υ , {3, 6}, 1) difference family for each prime power υ ≡ 1 (mod 36) and υ ⩾ 37. An infinite class of optimal frequency-hopping sequence is then obtained.