scholarly journals Improved upper bounds for the star discrepancy of digital nets in dimension 3

2003 ◽  
Vol 108 (2) ◽  
pp. 167-189 ◽  
Author(s):  
Friedrich Pillichshammer
Keyword(s):  
Upper Bounds ◽  
Star Discrepancy ◽  
Digital Nets

Construction Algorithms for Digital Nets with Low Weighted Star Discrepancy

2005 ◽  
Vol 43 (1) ◽  
pp. 76-95 ◽  
Author(s):  
Josef Dick ◽  
Gunther Leobacher ◽  
Friedrich Pillichshammer
Keyword(s):  
Star Discrepancy ◽  
Construction Algorithms ◽  
Digital Nets

Weighted Star Discrepancy of Digital Nets in Prime Bases

2006 ◽  
pp. 77-96 ◽  
Author(s):  
Josef Dick ◽  
Harald Niederreiter ◽  
Friedrich Pillichshammer
Keyword(s):  
Star Discrepancy ◽  
Digital Nets

The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬ s

2021 ◽  
Vol 16 (1) ◽  
pp. 71-92
Author(s):  
Tsvetelina Petrova
Keyword(s):  
Upper Bounds ◽  
Function System ◽  
Trigonometric Sum ◽  
Star Discrepancy

Abstract In the present paper the author uses the function system Γ ℬ s constructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an arbitrary net in the terms of the trigonometric sum of this net with respect to the functions of this system. The obtained estimations are inequalities of the type of Erdős-Turán-Koksma. These inequalities are very suitable for studying of nets constructed in the same Cantor system.

Digital Nets and Sequences

2009 ◽  
Author(s):  
Josef Dick ◽  
Friedrich Pillichshammer
Keyword(s):  
Digital Nets

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

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