Maximal arc partitions of designs

It is known that the designs PGn-1(n,q) in some cases have spreads of maximal α-arcs. Here a α-arc is a non-empty subset of points that meets every hyperplane in 0 or α points. The situation for designs in general is not so well known. This paper establishes an equivalence between the existence of a spread of α-arcs in the complement of a Hadamard design and the existence of an affine design and a symmetric design which is also the complement of a Hadamard design.