Abstract
We fully update the existence problem of orthogonal designs in order 16.
It is interesting to note that all n variable designs in order 16 for n=1,2,…,5 and all 6 and 7 variable designs which exist can be constructed from known 8 and 9 variable designs.
Keywords
- Variable Design
- Quadratic Form
- Orthogonal Design
- Existence Problem
- Multilinear Algebra
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Anthony V. Geramita, Joan Murphy Geramita, Jennifer Seberry Wallis, Orthogonal designs, Linear and Multilinear Algebra
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Peter J. Robinson, Some results on orthogonal designs
Peter J. Robinson, Amicable orthogonal designs
D. Shapiro, private communication (1975).
Jennifer Seberry Wallis, On the existence of Hadamard matrices, J. Combinatorial Th. Ser. A. (to appear).
Warren W. Wolfe, Rational quadratic forms and orthogonal designs, (Queen’s Math. Preprint No. 1975–22).
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© 1976 Springer-Verlag
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Robinson, P.J. (1976). Orthogonal designs in order sixteen. 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/BFb0097381
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DOI: https://doi.org/10.1007/BFb0097381
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08053-4
Online ISBN: 978-3-540-37537-1
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