Affine designs and linear orthogonal arrays

AbstractIt is proved that the collection of blocks of an affine 1-design that yields a linear orthogonal array is a union of parallel classes of hyperplanes in a finite affine space. In particular, for every prime power q and every m⩾2 there exists a unique (up to equivalence) complete linear orthogonal array of strength two associated with the classical design of points and hyperplanes in AG(m,q)