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Statistica Sinica 6(1996), 975-987


AN INFINITE SERIES OF ADJUSTED ORTHOGONAL

DESIGNS WITH REPLICATION TWO


Sunanda Bagchi


Indian Statistical Institute


Abstract: We construct a series of adjusted orthogonal designs with n+1 rows, 2n columns and n2+n treatments, where n is an integer other than 6. It is shown that members of this series are E-optimal when n>=5. This is the first series of adjusted orthogonal designs with constant replication number, and that too, at the minimum possible level. We also provide efficient designs in the cases n=2,3 and 4. The column designs of the above series are not regular graph designs. Since they are shown to be E-optimal, they provide an infinite series of counter examples to John and Mitchell's (1977) conjecture.



Key words and phrases: Adjusted orthogonal design, row-column design, rectangular design, E-optimality, regular graph design.



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