Super-simple group divisible designs with block size 4 and index 2

Super-simple group divisible designs are useful for constructing other types of super-simple designs which can be applied to codes and designs. In this article, we investigate the existence of a super-simple (4,2)-GDD of type gu and show that such a design exists if and only if u ⩾ 4 , g ( u − 2 ) ⩾ 4 , g ( u − 1 ) ≡ 0 ( mod 3 ) and u ( u − 1 ) g 2 ≡ 0 ( mod 6 ) .