Two-Dimensional Minimax Latin Hypercube Designs

Research output: Working paperDiscussion paperOther research output

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Abstract

We investigate minimax Latin hypercube designs in two dimensions for several distance measures.For the l-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n.For the l1-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n.We conjecture that the obtained lower bound is attained, except for a few small (known) values of n.For the l2-distance we have generated minimax solutions up to n = 27 by an exhaustive search method.The latter Latin hypercube designs will be included in the website www.spacefillingdesigns.nl.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages13
Volume2005-105
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper
Volume2005-105

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Latin Hypercube Design
Minimax
Covering Radius
Lower bound
Exhaustive Search
Distance Measure
Search Methods
Two Dimensions

Keywords

  • minimax
  • Latin hypercube designs
  • circle coverings

Cite this

van Dam, E. R. (2005). Two-Dimensional Minimax Latin Hypercube Designs. (CentER Discussion Paper; Vol. 2005-105). Tilburg: Operations research.
van Dam, E.R. / Two-Dimensional Minimax Latin Hypercube Designs. Tilburg : Operations research, 2005. (CentER Discussion Paper).
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van Dam, ER 2005 'Two-Dimensional Minimax Latin Hypercube Designs' CentER Discussion Paper, vol. 2005-105, Operations research, Tilburg.

Two-Dimensional Minimax Latin Hypercube Designs. / van Dam, E.R.

Tilburg : Operations research, 2005. (CentER Discussion Paper; Vol. 2005-105).

Research output: Working paperDiscussion paperOther research output

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N2 - We investigate minimax Latin hypercube designs in two dimensions for several distance measures.For the l-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n.For the l1-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n.We conjecture that the obtained lower bound is attained, except for a few small (known) values of n.For the l2-distance we have generated minimax solutions up to n = 27 by an exhaustive search method.The latter Latin hypercube designs will be included in the website www.spacefillingdesigns.nl.

AB - We investigate minimax Latin hypercube designs in two dimensions for several distance measures.For the l-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n.For the l1-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n.We conjecture that the obtained lower bound is attained, except for a few small (known) values of n.For the l2-distance we have generated minimax solutions up to n = 27 by an exhaustive search method.The latter Latin hypercube designs will be included in the website www.spacefillingdesigns.nl.

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KW - circle coverings

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van Dam ER. Two-Dimensional Minimax Latin Hypercube Designs. Tilburg: Operations research. 2005. (CentER Discussion Paper).