# OA131: A 3D orthogonal array of strength 2 In DiceDesign: Designs of Computer Experiments

## Description

A 3-dimensional linear orthogonal array (OA) of strength 2 with 49 points. The design points are equally spaced into 2 dimensional coordinate planes. However by construction, such OAs satisfy a linear relation, here: `x1 + 3*x2 + x3 = 0 (mod 7)`. As a consequence, the design points are contained in parallel planes orthogonal to (1,3,1). Actually, they are also contained in parallel planes orthogonal to other directions, as (2,-1,2) or (3,2,3), since the congruence relation leads to `2*x1 - x2 + 2*x3 = 0 (mod 7)` or `3*x1 + 2*x2 + 3*x3 = 0 (mod 7)`. For instance, they are contained in 4 parallel planes orthogonal to (2,-1,2).

## Usage

 `1` ```data(OA131) ```

## Format

A data frame with 49 observations on the following 3 variables.

`x1`

first coordinate

`x2`

second coordinate

`x3`

third coordinate

## Source

Roustant O., Franco J., Carraro L., Jourdan A. (2010), A radial scanning statistic for selecting space-filling designs in computer experiments, MODA-9 proceedings.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```data(OA131) # centering and reducing to [0,1]^3 OA <- (OA131 + 0.5)/7 pairs(OA, xlim=c(0,1), ylim=c(0,1)) ## Not run: library(lattice) cloud(x3~x1+x2, data=OA, xlim=c(0,1), ylim=c(0,1), zlim=c(0,1), screen = list(z = 50, x = -70, y = 0)) ## End(Not run) ```

DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.