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We construct a class of special homogeneous Moran sets, called $\left\{m_k\right\}$-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of ${\left\{m_k\right\}}_{k\ge 1}$, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.