Construction of main effects plans orthogonal through the block factor based on level permutation

In this paper, We first demonstrate that the orthogonal property of main effects plans orthogonal through the block factor (Bagchi, 2010) remains unchanged under level permutation. However, level permutation of factors could alter their geometrical structures and statistical properties. Hence uniformity is used to further distinguish main effects plans orthogonal through the block factor (POTB). A modified optimization algorithm is proposed to search uniform or nearly uniform POTBs and many new optimal POTBs with lower-discrepancy are obtained.