## Families of A-optimal block designs for comparing test treatments with a control.(English)Zbl 0586.62113

Authors’ abstract: A-optimal designs for comparing each of $$\nu$$ test treatments simultaneously with a control, in b blocks of size k each are considered. It is shown that several families of BIB designs in the test treatments augmented by t replications of a control in each block are A- optimal.
In particular these designs with $$t=1$$ are optimal whenever $$(k-2)^ 2+1\leq \nu \leq (k-1)^ 2$$ irrespective of the number of blocks. This includes BIB designs associated with finite projective and Euclidean geometries.
Reviewer: A.C.Tamhane

### MSC:

 62K05 Optimal statistical designs 62K10 Statistical block designs
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