OSOAs_hadamard: function to create a strength 3 OSOA with 8-level columns or...

In SOAs: Creation of Stratum Orthogonal Arrays

function to create a strength 3 OSOA with 8-level columns or a strength 3- OSOA with 4-level columns from a Hadamard matrix

Description

A Hadamard matrix in k runs is used for creating an OSOA in n=2k runs for at most m=k-2 columns (8-level) or m=k-1 columns (4-level).

Usage

OSOAs_hadamard(
  m = NULL,
  n = NULL,
  el = 3,
  noptim.rounds = 1,
  noptim.repeats = 1,
  optimize = TRUE,
  dmethod = "manhattan",
  p = 50
)

Arguments

m	the number of columns to be created; if n is also given, m must be compatible with it; at present, m can be at most 98.
n	the number of runs to be created; n must be a multiple of 8 and can (at present) be at most 200; if m is also given, n must be compatible with it.
el	exponent for 2, can be 2 or 3: the OSOA will have columns with 2^el (4 or 8) levels
noptim.rounds	the number of optimization rounds for each independent restart
noptim.repeats	the number of independent restarts of optimizations with noptim.rounds rounds each
optimize	logical: should space filling be optimized by level permutations?
dmethod	distance method for phi_p, "manhattan" (default) or "euclidean"
p	p for phi_p (the larger, the closer to maximin distance)

Details

At least one of m or n must be provided. For el=2, Zhou and Tang (2019) strength 3- designs are created, for el=3 strength 3 designs by Li, Liu and Yang (2021).
Li et al.'s creation of the matrix A has been enhanced by using a column specific fold-over, which is beneficial for the space-filling properties (see Groemping 2022).

Value

matrix of class SOA with the attributes that are listed below. All attributes can be accessed using function attributes, or individual attributes can be accessed using function attr. These are the attributes:

type

the type of array (SOA or OSOA)

strength

character string that gives the strength

phi_p

the phi_p value (smaller=better)

optimized

logical indicating whether optimization was applied

permpick

matrix that lists the id numbers of the permutations used

perms2pickfrom

optional element, when optimization was conducted: the overall permutation list to which the numbers in permlist refer

call

the call that created the object

Author(s)

Ulrike Groemping

References

For full detail, see SOAs-package.

Groemping (2023a)
Li, Liu and Yang (2021)
Weng (2014)
Zhou and Tang (2019)

Examples

dim(OSOAs_hadamard(9, optimize=FALSE))  ## 9 8-level factors in 24 runs
dim(OSOAs_hadamard(n=16, optimize=FALSE)) ## 6 8-level factors in 16 runs
OSOAs_hadamard(n=24, m=6, optimize=FALSE) ## 6 8-level factors in 24 runs
                                          ## (though 10 would be possible)
dim(OSOAs_hadamard(m=35, optimize=FALSE)) ## 35 8-level factors in 80 runs

SOAs documentation built on Sept. 9, 2025, 5:40 p.m.