Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares

Abstract

t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t treatments (t  2) occur together is a constant. Like other families of incomplete block designs, t-designs find potential application in farming system research where the main concern would be to select the best combination out of a certain set of t-component farming systems for a specific agro-ecological zone. But in order to obtain t-balance we may require large number of blocks and replications. Partially balanced t-designs are introduced for experimental situations where it is not possible to get t-balanced designs. A series of partially balanced 3-designs are constructed using mutually orthogonal Latin Squares. These designs, though possess pair-wise balance, are not combinatorially balanced in terms of 3-tuples. They also satisfy the properties of 3-packing designs. The efficiency factor of these designs is quite high as v increases, the efficiency increases.