All triples for orthogonal designs of order 40

All triples for orthogonal designs of order 40

The use of amicable sets of eight circulant matrices and four negacyclic matrices to generate orthogonal designs is relatively new. We find all 1841 possible orthogonal designs of order 40 in three variables, using only these new techniques.

On amicable orthogonal designs of order 8

Some new amicable orthogonal designs of order 8 are found as part of a complete search of the equivalence classes for orthogonal designs OD(8; 1, 1, 1, 1), OD(8; 1, 1, 1, 4), OD(8; 1, 1, 2, 2), OD(8; 1, 1, 1, 2), OD (8; 1, 1, 2, 4), OD(8; 1, 1, 1, 3), OD(8; 1, 1, 2, 3), OD(8; 1, 1, 1, 5) and OD(8; 1, 1, 3, 3). 2000 Mathematics subject classification (Amer. Math. Soc.): 05B30, 15A36.

On Full Orthogonal Designs in Order 56

We find new full orthogonal designs in order 56 and show that of 1285 possible OD(56; s1, s2, s3, 56—s1—s2-s3) 163 are known, of 261 possible OD(56; s1, s2, 56—s1—s2) 179 are known. All possible OD(56; s1, 56 — s1) are known. Keywords : Construction, sequences, circulant matrices, amicable sets, orthogonal designs, AMS Subject Classification: Primary 05B15, 05B20, Secondary 62K05. Publication D...

Some new orthogonal designs in orders 32 and 40

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.

Decomposing triples into cyclic designs