Minimum variance orthogonal covariate block designs with improved position-balance

Covariate designs are extensively used to enhance the precision and efficiency pertaining to the estimation of parameters of interest. Minimum variance orthogonal covariate block designs (MV-OCBDs) maintain orthogonality among treatment, block, and covariate effects while minimizing variance, thereby yielding highly efficient estimators. In this study, MV-OCBDs are systematically constructed using reshuffled blocks of base designs through M arrays, L matrices, orthogonal integer arrays and Hadamard matrices. This reshuffling ensures position-balance, i.e., uniform spread of treatments at each unit position, thereby eliminating possible bias in treatment allotment. Thus, position balance directly parallels the space-filling property, where treatments must be spread uniformly over all positions in a block to capture spatial heterogeneity. In addition, an R package has also been developed for the generation of MV-OCBDs to broaden its application potential in diverse fields of research.