Super-simple group divisible designs with block size 4 and index 5

In this paper, we investigate the existence of a super-simple (4, 5)-GDD of type g u and show that such a design exists if and only if u ≥ 4 , g ( u − 2 ) ≥ 10 , g ( u − 1 ) ≡ 0 ( mod 3 ) and u ( u − 1 ) g 2 ≡ 0 ( mod 12 ) .