Construction of Partially Balanced Semi-Latin Rectangles with Block Size 4

Semi-Latin rectangles represent row-column designs where each row-column intersection contains the same number of experimental units, denoted as k >1. Additionally, each treatment appears an equal number of times in each row ( r n , say) and in each column ( c n , say) ( 1 r n ≥ and 1 c n ≥ may or may not be same). Partially Balanced Semi-Latin rectangles (PBSLR) constitute a subset of Semi-Latin rectangles (SLR), serving as generalizations of Latin squares and Semi-Latin squares (SLS). These designs find utility in various agricultural and industrial experiments, particularly situations where one effect is considered a column effect and the other a row effect, with the intersection (block/cell) accommodating precisely four units. This article introduces two methods for constructing PBSLR designs with a block size of 4. Also, R package has been developed for generating the designs.