We describe the construction of a piecewise polynomial generator over a Galois ring and prove a transitivity criterion for it. We give an estimate for the discrepancy of the output sequences of such a generator. We show that the obtained estimate is asymptotically equivalent to known estimates for special cases of a piecewise polynomial generator, and in some cases it is asymptotically sharper.

中文翻译：

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Galois环上的分段多项式序列

我们描述了在Galois环上的分段多项式生成器的构造，并证明了它的传递性准则。我们给出了这种生成器的输出序列差异的估计。我们显示，对于分段多项式生成器的特殊情况，获得的估计值渐近等效于已知的估计值，在某些情况下，它的渐近尖锐性。