2003, Volume 65, Pt. 3, 641--648

**The “Best” Of The Three Optimal (4
Times 4)/4 Semi-Latin Squares**

By

POLY E. CHIGBU, University of Nigeria, Nsukka, Nigeria

SUMMARY. Currently, there exist three optimal (4$\times$4)/4 semi-Latin squares for sixteen treatments in blocks of size four. Since these squares do not have the same concurrences, there is a need for distinguishing one square from the others and determining the most preferred square in a given context. This work ascertains the ``best" square by finding and comparing the variances of elementary contrasts of treatments for the squares.

*AMS (1991) subject classification. *62K10, 05B15, 62K05.

*Key words and phrases. *Concurrences, Efficiency factors, Optimality,
semi-Latin square.