Maria Rita Iacò, Volker Ziegler
Published 2015-03-25Version 1
The $LS$-sequences are a parametric family of sequences of points in the unit interval. They were introduced by Carbone, who also proved that under an appropriate choice of the parameters $L$ and $S$, such sequences are low-discrepancy. The aim of the present paper is to provide explicit constants in the bounds of the discrepancy of $LS$-sequences. Further, we generalize the construction of Carbone and construct a new class of sequences of points in the unit interval, the generalized $LS$-sequences.
One example of singular representations of real numbers from the unit interval
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On partitions of the unit interval generated by Brocot sequences
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