### Abstract

First, we propose a notion of (t,e,s)-sequences in base b, where e is an integer vector (e_{1},.,e_{s}) with e_{i}≥1 for i=1,.,s, which are identical to (t,s)-sequences in base b when e=(1,.,1), and show that a generalized Niederreiter sequence in base b is a (0,e,s)-sequence in base b, where ^{ei} is equal to the degree of the base polynomial for the i-th coordinate. Then, by using the signed splitting technique invented by Atanassov, we obtain a discrepancy bound for a (t,e,s)-sequence in base b. It follows that a (unanchored) discrepancy bound for the first N>1 points of a generalized Niederreiter sequence in base b is given as ND_{N}≤(1/ s!aπi=1s2Š^{bei}/2^{ei}logb)(logN) ^{s}+O((logN)^{s-1}), where the constant in the leading term is asymptotically much smaller than the one currently known.

Original language | English |
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Pages (from-to) | 240-247 |

Number of pages | 8 |

Journal | Journal of Complexity |

Volume | 29 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Jan 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- Mathematics(all)
- Control and Optimization
- Applied Mathematics

### Cite this

*Journal of Complexity*,

*29*(3-4), 240-247. https://doi.org/10.1016/j.jco.2013.02.001