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Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base $b$ and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form $P\left(i\right)=ai(modb)$ for coprime integers $a$ and $b$. We show that multipliers $a$ that either divide $b-1$ or $b+1$ generate van der Corput sequences with weak...