$A$-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.
@article{1176349552,
author = {Hedayat, A. S. and Majumdar, Dibyen},
title = {Families of $A$-Optimal Block Designs for Comparing Test Treatments with a Control},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 757-767},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349552}
}
Hedayat, A. S.; Majumdar, Dibyen. Families of $A$-Optimal Block Designs for Comparing Test Treatments with a Control. Ann. Statist., Tome 13 (1985) no. 1, pp. 757-767. http://gdmltest.u-ga.fr/item/1176349552/