Some new orthogonal designs in orders 32 and 40 Original Research Article

A result of Robinson states that no OD(n;1,1,1,1,1,n−5) exists for n>40. We complement this result by showing the existence of OD(n;1,1,1,1,1,n−5) for n=32,40. This includes a resolution to an old open problem regarding orthogonal designs of order 32 as well. We also obtain a number of new orthogonal designs of order 32.