Frames with block size four and index three

Abstract A (k,λ)-frame of type hu is a (k,λ)-GDD ( X , G , A ) of type hu in which the collection of blocks A can be partitioned into partial parallel classes each of which partitions X −G i for some G i ∈ G . In this paper, we investigate the existence of (4,3)-frames of type hu and show that the necessary conditions are also sufficient with a small number of possible exceptions.