Orthogonal Designs in powers of two

Repeat designs are introduced and it is shown how they may be used to give very powerful constructions for orthogonal designs in powers of two. These results are used to show all full four variable and all three variable designs exist in 2t , t ≤ 9. We believe these constructions demonstrate the existence of all possible four variable designs with no zeros in every power of two but we have not been able to prove this.