Small,balanced, efficient and near rotatable central composite designs

Standard central composite designs for fitting second-order models usually have a large number of design points, especially when the number of factors under consideration is large. In this paper we propose small, balanced and near rotatable central composite designs reducing the design's size and maintaining the ability to estimate all the model parameters. We list the best designs we identified to accommodate 4?k?9$4?k?9$ experimental factors. A detailed comparison between our findings and already known second-order designs has also been made.