Rotatability is a property that requires that the variance of estimates of responses at points equidistant from the centre of the design is constant on circles or spheres or hyper-spheres. The study of rotatable designs mainly emphasises the estimation of the absolute response. In this study, the aim was to construct second order rotatable designs in three, four, five, six and k-factors based on balanced incomplete block designs. The main objective was to obtain the variance and covariances of parameter estimates of the second-order experimental designs. Using a balanced incomplete block design in three, four, five, six, and k-factors where each factor will contain two treatments, factorial combinations were obtained. An incidence matrix of Balanced Incomplete Block Design is suitably chosen and must satisfy the necessary Balanced Incomplete Block Design conditions. It should also satisfy the non-singularity conditions for a second-order design to be rotatable. A set of points was also suitably chosen and used to denote the symmetric point sets associated with an appropriate, balanced incomplete design. In conclusion, some new second-order rotatable designs in three, four, five and six factors and their generalisation in factors were obtained through balanced incomplete block designs.
