Affiliation:
1. Hong Kong Baptist Univ., Kowloon Tong, Hong Kong
Abstract
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Science Applications,Modelling and Simulation
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