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), 0≤e+f+g≤32 are the types of orthogonal designs in order 32.
These results 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.
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References
Anthony V. Geramita, Joan Murphy Geramita, Jennifer Seberry Wallis, Orthogonal designs, Linear and Multilinear Algebra, (to appear).
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Warren W. Wolfe, Orthogonal designs-amicable orthogonal designs-some algebraic and combinatorial techniques, Ph.D. Dissertation, Queen’s University, Kingston, Ontario, 1975.
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© 1976 Springer-Verlag
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Geramita, A.V., Wallis, J.S. (1976). Some new constructions for orthogonal designs. In: Casse, L.R.A., Wallis, W.D. (eds) Combinatorial Mathematics IV. Lecture Notes in Mathematics, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097367
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DOI: https://doi.org/10.1007/BFb0097367
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