ORTHOGONAL COLLECTIONS OF LATIN SQUARES

The row-column setting for comparing upsilon experimental treatments i s a p x q array of experimental units, with the p rows and q columns r epresenting levels of two blocking factors. When p = q = upsilon, the optimal design for estimating treatment contrasts is a Latin square. F or a vt factorial treatment set in the same setting, t mutually orthog onal Latin squares are an optimal main-effects plan. Orthogonal collec tions of Latin squares arise when these results are generalized to b r ow-column layouts of size upsilon x upsilon, where b is greater than 1 . This article studies these orthogonal collections, with special emph asis on small upsilon and b.