DiceDesign (version 1.10)

OA131: A 3D orthogonal array of strength 2

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

data(OA131)

Format

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

x1

first coordinate

x2

second coordinate

x3

third coordinate

Examples

data(OA131)

# centering and reducing to [0,1]^3
OA <- (OA131 + 0.5)/7
pairs(OA, xlim=c(0,1), ylim=c(0,1))

if (FALSE) {
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))}