Experimental designs using digital nets with small numbers of points

Kwong Ip Liu, Fred J. Hickernell

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

Abstract

Digital nets can improve upon traditional fractional factorial designs because for a budget of n=bm runs, they can allow b, …, bm−1, or bm levels per factor, while retaining the good balance properties of orthogonal arrays. However, the t-value typically used to characterize the quality of digital nets is not adequate for the purposes of experimental design. Rather, concepts from the experimental design literature, such as strength, resolution and aberration should be used. Moreover, the known number-theoretic constructions of digital nets are optimized for large m, whereas for laboratory experiments one typically has n=bm less than 100.

This article describes some recent work on constructing digital nets with small numbers of points that are suitable for experimental designs. Coding theory provides some bounds on the quality of designs that may be expected. The generating matrices for the designs are found by computational search. The quality of the designs obtained is compared with the coding theory bounds.
Original languageEnglish
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods 2004
EditorsHarald Niederreiter, Denis Talay
PublisherSpringer Berlin Heidelberg
Pages343–354
Number of pages12
Edition1st
ISBN (Electronic)9783540311867
ISBN (Print)9783540255413
DOIs
Publication statusPublished - Feb 2006
Event6th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2004 - Juan-les-Pins, France
Duration: 7 Jun 200410 Jun 2004
https://link.springer.com/book/10.1007/3-540-31186-6 (Link to conference proceedings)

Conference

Conference6th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCMQC 2004
Country/TerritoryFrance
CityJuan-les-Pins
Period7/06/0410/06/04
Internet address

User-Defined Keywords

  • Orthogonal Array
  • Generate Matrice
  • Test Vector
  • Candidate Vector
  • Strength Table

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