The existence of (q,k,λ,t)-ADFs for k=4,5,6

Almost difference families ((q,k,λ,t)-ADFs) were introduced by Ding and Yin as an useful generalization of almost difference sets (ADSs), constructions and infinite classes of almost difference families were also presented. In this paper, several new infinite classes of (q,k,λ,t)-ADFs for k=4, 5 and 6 are constructed.