Abstract
First, we propose a notion of (t,e,s)-sequences in base b, where e is an integer vector (e1,.,es) with ei≥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 NDN≤(1/ s!aπi=1s2Šbei/2eilogb)(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 - 2013 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- Mathematics(all)
- Control and Optimization
- Applied Mathematics