# Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs

@article{Wang2018OptimalM, title={Optimal maximin \$L\_\{1\}\$-distance Latin hypercube designs based on good lattice point designs}, author={Lin Wang and Qian Xiao and Hongquan Xu}, journal={The Annals of Statistics}, year={2018}, url={https://api.semanticscholar.org/CorpusID:13671361} }

This work constructs a series of maximin Latin hypercube designs via Williams transformations of good lattice point designs that are optimal under the maximin L1-distance criterion, while others are asymptotically optimal.

## 45 Citations

### Optimal maximin L2-distance Latin hypercube designs

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### Construction of Flexible Maximin Latin Hypercube Designs Based on Good Lattice Point Sets

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This paper would like to further this idea for more general, or more flexible, designs, such as N equal to primes, prime multiples and prime powers, and implement a similar construction algorithm to build optimal or asymptotically optimal designs of such dimension.

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A new non-iterative deterministic algorithm for constructing asymptotically orthogonal maximin distance LHDs and an iterative algorithm utilizing a mixture of criteria is provided for further improvement of the performance of the newly constructed L HDs from multiple perspectives.

### Musings about Constructions of Eﬃcient Latin Hypercube Designs with Flexible Run-sizes

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Using the R package which integrates and improves various algebraic and searching methods, many of the designs found in this paper are better than the existing ones and can serve as benchmarks for the future developments on LHDs.

### A Construction Method for Maximin L1-Distance Latin Hypercube Designs

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A Construction Method for Maximin L1-Distance Latin Hypercube Designs

### LHD: An R package for efficient Latin hypercube designs with flexible sizes

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The R package LHD is developed that integrates and improves various algebraic and searching methods to construct efficient LHDs with flexible design sizes and many of the designs found in this paper are better than the existing ones.

### A method of constructing maximin distance designs

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The basic idea is to construct large designs from small designs and the method is effective because the quality of large designs is guaranteed by that of small designs, as evaluated by the maximin distance criterion.

### New bounds and search for maximin distance U‐type designs

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This study obtains a new upper bound for the separation distance of certain classes of five‐level U‐type designs, investigates the characteristics of maximin distance U‐type designs and shows the optimality of some existing orthogonal designs.

### Connecting U-type Designs Before and After Level Permutations and Expansions

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This paper systematically study the theoretical properties of U-type designs before and after level permutations and expansions, and establishes the relationships between the initial designs’ generalized word-length patterns (GWLP) and the generated designs' orthogonal and space-filling properties.

## 33 References

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Mathematics, Computer Science

Based on number theory and finite fields, three algebraic methods to construct maximin distance Latin squares as special Latin hypercube designs are proposed and lower bounds on their minimum distances are developed.

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Mathematics

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Mathematics, Computer Science

A new, well-performing algorithm is presented for the construction of maximin Latin hypercube designs using a 2-dimensional distance metric and an additional criterion, design orthogonality, is important when screening the effects of the input variables and a new search algorithm for orthogonal maximin designs is described.

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Mathematics

Latin hypercube designs have found wide application. Such designs guarantee uniform samples for the marginal distribution of each input variable. We propose a method for constructing orthogonal Latin…

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Computer Science, Mathematics

Latin hypercube designs suitable for factor screening are presented and they are shown to be efficient in terms of runs required per factor as well as having optimal and orthogonal properties.

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Mathematics, Computer Science

The method generates orthogonal Latin hypercube designs that can include many more factors than those proposed by Ye (1998) and can also be used to construct Latin hyper cube designs with low correlation of first-order and second-order terms.

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Mathematics, Computer Science

A new construction approach is developed that first generates the small Latin hypercube design in each slice and then arranges them together to form the SLHD.

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Mathematics, Computer Science

An algorithm for constructing orthogonal Latin hypercubes, given a fixed sample size, in more dimensions than previous approaches is presented, and a method that dramatically improves the space-filling properties of the resultant Latinhypercubes is detailed.

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Mathematics, Computer Science

It is proved that when used for integration, the sampling scheme with OA-based Latin hypercubes offers a substantial improvement over Latin hypercube sampling.

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Computer Science, Mathematics

An approach to constructing 2 r -order orthogonal LHDs with 2 r+1 +2 runs and 2 r factors has the minimum correlation between any two distinct columns.