Algorithms for the construction of (M,S)-optimal block designs and row-column designs

Abstract

Algorithms for the generation of (M, S)optimal block and row-column designs are presented. The first algorithm generates the treatment-block incidence matrix of an (M, S)-optimal block design. The second searches for the particular permutation of the rows of an incidence matrix which gives the best possible combination of rows and columns within the row-column design. A row-column design is then obtained by combining the selected treatment-row and treatment-column arrangements using the method of Systems of Distinct Representatives.

Keywords:

• Algorithms
• block designs
• construction
• (M, S)-optimality
• relative efficiency
• row-column designs
• systems of distinct representatives