Abstract
We give three new constructions for orthogonal designs using amicable orthogonal designs. These are then used to show (i) all possible n-tuples, n ~ 5 , are the types of orthogonal designs in order 16 and (ii) all possible n-tuples, n ~ 3 are the types of orthogonal designs in order 32 , (iii) all 4-tuples, (e, f, g, 32-e-f-g) , o ~ e T f T g ~ 32 are the types of orthogonal designs in order 32. These resultg are used in a paper by Peter J. Robinson, "Orthogonal designs of order sixteen", in this same volume, to fully update the status of the existence of orthogonal designs in order 16
Publication Details
Geramita, AV and Seberry, J, Some new constructions for orthogonal designs, Combinatorial Mathematics IV, Lecture Notes in Mathematics, 560, 1976, 46-54.