Maximal arc partitions of designs Original Research Article

It is known that the designs image in some cases have spreads of maximal image-arcs. Here a image-arc is a non-empty subset of points that meets every hyperplane in 0 or image points. The situation for designs in general is not so well known. This paper establishes an equivalence between the existence of a spread of image-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.