# createAddelKemp3: Create an orthogonal array using the Addelman-Kempthorne... In lhs: Latin Hypercube Samples

## Create an orthogonal array using the Addelman-Kempthorne algorithm with `2q^3` rows.

### Description

The `addelkemp3` program produces `OA( 2*q^3, k, q, 2 )`, `k <= 2q^2+2q+1`, for prime powers `q`. `q` may be an odd prime power, or `q` may be 2 or 4.

### Usage

```createAddelKemp3(q, ncol, bRandom = TRUE)
```

### Arguments

 `q` the number of symbols in the array `ncol` number of parameters or columns `bRandom` should the array be randomized

### Details

From Owen: An orthogonal array `A` is a matrix of `n` rows, `k` columns with every element being one of `q` symbols `0,...,q-1`. The array has strength `t` if, in every `n` by `t` submatrix, the `q^t` possible distinct rows, all appear the same number of times. This number is the index of the array, commonly denoted `lambda`. Clearly, `lambda*q^t=n`. The notation for such an array is `OA( n, k, q, t )`.

### Value

an orthogonal array

### References

Owen, Art. Orthogonal Arrays for: Computer Experiments, Visualizations, and Integration in high dimenstions. http://lib.stat.cmu.edu/designs/oa.c. 1994 S. Addelman and O. Kempthorne (1961) Annals of Mathematical Statistics, Vol 32 pp 1167-1176.

```A <- createAddelKemp3(3, 3, TRUE)