On super-simple group divisible designs with block size four and index

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