Resolvable group divisible designs with block size four and general index

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type hnhn and general index λλ. The necessary conditions for the existence of such a design are n≥4n≥4, hn≡0(mod4) and λh(n−1)≡0(mod3). These necessary conditions are shown to be sufficient for all λ≥2λ≥2, with the definite exceptions of (λ,h,n)∈{(3,2,6)}∪{(2j+1,2,4):j≥1}(λ,h,n)∈{(3,2,6)}∪{(2j+1,2,4):j≥1}. The known existence result for λ=1λ=1 is also improved.