Abstract
It is known that the designs
PG
n
-
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.