Two-level factorial designs in block size four

Two-level factorial designs are widely used to identify significant effects in agriculture and allied fields. The occurrence of practical constraints, which can make it necessary to arrange runs in small block size like block size four, provide a major motivation for work in this area. Investigating the optimal number of replications needed to be carried out to estimate important factorial effects for factorial experiments with blocks of size four has attracted considerable interest from researchers. Estimating all main effects and two-factor interactions in a two-level factorial experiment in blocks setup, obtaining precise estimates generally requires a significant number of replications. The article presents methodologies aimed at obtaining efficient block designs for two-level factorial experiments in block size 4, which hold potential for improving the efficiency factor and effectiveness of experimental investigations.