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(mod3) and u(u−1)g2≡0(mod6).