Construction of main-effect plans orthogonal through the block factor

Bagchi (2010) proposed main-effect plans orthogonal through the block factor (POTB), in which the treatment factors are pairwise orthogonal through the block factor. However, not many construction methods are available in the literature. In this paper, we present several new construction approaches for saturated POTBs with small runs and mixed levels. Moreover, all of them are connected and variance-balanced.