The augmented block design is widely used in breeding programs, particularlyrnin screening and selection of a large number of germplasm lines with non-replicatedrntest treatments and replicated control treatments to estimate the experimental error. Thernstudy establishes a relationship between augmented design via RIB design and designsrnfor test treatment(s) versus control treatment(s) and 2v balanced main effect plansrn(saturated and unsaturated) obtained through BIB designs. The data used in this studyrnwere obtained from an experiment of wheat which was conducted by using augmentedrnRIB design and a modified augmented BIB design from scientific journal. In theserndesign, we consider eight test treatments and four control treatment for augmentedrndesign and thirteen test treatment and three control treatment for the modifiedrnaugmented BIB design. The construction and the analysis of modified augmented BIBrndesign can be considered by using the fixed and mixed model analysis, and in addition,rna method is proposed for finding A- and MV- Optimal designs such situations andrnsome sufficient conditions are given under which a design obtained using the proposedrnmethod will be A-and MV-optimal. Some examples are also given to show how thernresults obtained can be applied. The results were obtained using excel and SAS. Wernhave seen in this study that when block is greater than two, the modified augmentedrnBIB design is more efficient than augmented RIB designs.rnKey words: Augmented Design, Modified Augmented Block Design, Fixed EffectrnModel and Random Effect Model