Construction of Balanced Semi-Latin Rectangles in block size four: An Algorithmic Approach

Semi-Latin rectangles are row-column designs in which each row-column intersection has same number of experimental units, say k > 1 and each treatment appears same number of times in each row and same number of times in each column. Balanced Semi-Latin rectangles (BSLR) are the subclass of Semi-Latin rectangles (SLR) which are generalizations of Latin squares and Semi-Latin squares (SLS). Such types of designs are more useful in various agricultural as well as industrial experiments in which one of the effects can be consider as column effect and another as row effect, where the intersection of effects can only accommodate 4 units. This article proposes an algorithm to construct BSLR designs with a block size of four.