On super-simple group divisible designs with block size four and index λ=3,4,6λ=3,4,6

In this paper, we show that the necessary conditions for the existence of a super-simple (4,λ)-GDD(4,λ)-GDD of type gugu with λ∈{3,4,6}λ∈{3,4,6} are also sufficient except for (λ,g,u)∈{(3,2,5),(4,3,5)}(λ,g,u)∈{(3,2,5),(4,3,5)}.