Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series B, Pt. 1, pp. 112--121

E-OPTIMAL NESTED ROW-COLUMN DESIGNS WITH UNEQUAL REPLICATIONS OF TREATMENTS

By

NIZAM UDDIN,  Tennessee Technological University

and

SYED A. HOSSAIN, University of Nebraska at Kearnay

SUMMARY.  Simple sufficient conditions are obtained for E-optimal nested row-column designs and some methods of constructions are developed. It is shown that whenever universally optimal nested row-column designs extended by certain block exists it is E-optimal. Also it is shown that the individual blocks of certain universally optimal nested row-column designs can be augmented by additional columns to obtain E-optimal designs. A table of E-optimal designs obtained by trial and error for $v \leq 12$ is given.

AMS subject classification.  Primary 62K05, secondary 62K10.

Key words and phrases. Balanced incomplete block designs, efficiency, $E$-optimality, finite field, group divisible designs method of differences, nested row-column designs.

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