Universally optimal structurally balanced row–column designs with some empty nodes.

*(English)*Zbl 1065.62137Summary: We present two methods of construction of a class of universally optimal \(b_1\times b_2\) row-column designs with \(b_2-k_1>0\) empty nodes in each row and \(b_1-k_2>0\) empty nodes in each column. The number of treatments under consideration is of the form \(s+1\) where \(s\) is an odd prime power number. The designs constructed here are structurally balanced in the sense that every pair of columns is used in an equal number of rows. The proposed designs can also be used as universally optimal two-factor orthogonal main-effect plans arranged in incomplete blocks which are also equivalent to orthogonal pairs of balanced incomplete block designs, balanced incomplete block designs for two sets of treatments, and two stage experiments in incomplete blocks with different numbers of treatments for the two stages.

##### Keywords:

Balanced incomplete block design; Difference sets; Multistage experiments; Orthogonal main-effect plan; Structural balance; Structurally incomplete row-column design; Universal optimality
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\textit{N. Uddin}, J. Stat. Plann. Inference 133, No. 2, 509--522 (2005; Zbl 1065.62137)

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##### References:

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