FAURE H.

Fred J. Hickernell

NIEDERREITER H.

OWEN A. B.

ROTH K.F.

SACKS J.

WARNOCK T. T.

WOZNIAKOWSKI H.

ZAREMBA S. K.


            One popular family of low dicrepancy sets is the (
            t, m, s
            )-nets. Recently a randomization of these nets that preserves their net property has been introduced. In this article a formula for the mean square
            L
            2
            -discrepancy of (
            0, m, s
            )-nets in base
            b
            is derived. This formula has a computational complexity of only O(s log(
            N
            ) + s
            2
            ) for large
            N
            or s, where
            
              N = b
              m
            
            is the number of points. Moreover, the root mean square
            L
            2
            -discrepancy of (
            0, m, s
            )-nets is show to be O(
            N
            -1
            [log(N)]
            (s-1)/2
            ) as
            N
            tends to infinity, the same asymptotic order as the known lower bound for  the
            L
            2
            -discrepancy of an arbitrary set.
          </jats:p

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ACM Transactions on Modeling and Computer Simulation

The mean square discrepancy of randomized nets

The mean square discrepancy of randomized nets

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