Balanced incomplete block designs are not always possible to construct because of their parametric relations. In such a situation another balanced design, the variance balanced design, is required. This construction of binary, equal replicated variance balanced designs are discussed using the half fraction of the 2n factorial designs with smaller block sizes. This method was also extended to construct another variance balanced design by deleting the last block of the resulting variance balanced designs. Its efficiency factor compared with randomized block designs was compared and found to be highly efficient.
Ghosh, D. K., & Ahuja, S. (2017). On Variance Balanced Designs. Journal of Modern Applied Statistical Methods, 16(2), 124-137. doi: 10.22237/jmasm/1509494820