Non-validity of affine α-resolvability in regular group divisible designs

The concept of affine α-resolvability has been discussed for block designs in literature since 1942 for α=1 and in particular since 1963 for α⩾2. Among group divisible (GD) designs, affine α-resolvable designs are known for both classes of singular GD and semi-regular GD designs. However, no example has been found for an affine α-resolvable regular GD design in literature. In this paper, the validity of such concept will be disproved for regular GD designs in general. Thus the regular GD design does not possess any property of the affine α-resolvability.