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Using product designs to construct orthogonal designs

Published online by Cambridge University Press:  17 April 2009

Peter J. Robinson
Peter J. Robinson
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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This paper produces new types of designs, called product designs, which prove extremely useful for constructing orthogonal designs. An orthogonal design of order 2t and type

is constructed. This design often meets the Radon bound for the number of variables.

We also show that all orthogonal designs of order 2t and type (a, b, c, d, 2t-a-b-c-d), with 0 < a + b + c + d < 2t, exist for t = 5, 6, and 7.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 297 - 305
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Geramita, Anthony V., Geramita, Joan Murphy and Wallis, Jennifer Seberry, “Orthogonal designs”, Linear and Multilinear Algebra 3 (1975/1976), 231–306.Google Scholar
[2]Geramita, Anthony V. and Wallis, Jennifer Seberry, “Some new constructions for orthogonal designs”, Combinatorial Mathematics IV, 46–54 (Proc. Fourth Austral. Conf., University of Adelaide, 1975. Lecture Notes in Mathematics, 560. Springer-Verlag, Berlin, Heidelberg, New York, 1976).CrossRefGoogle Scholar
[3]Robinson, Peter J., “Concerning the existence and construction of orthogonal designs”, (PhD thesis, Australian National University, Canberra, 1977).CrossRefGoogle Scholar
[4]Wolfe, Warren W., “Orthogonal designs - amicable orthogonal designs -some algebraic and combinatorial techniques”, (PhD Dissertation, Queen's University, Kingston, Ontario, 1975).Google Scholar