# Construction of Designs Based on Mutually Orthogonal Latin Squares

### Description

The function constructs row-column designs based on complete sets of mutually orthogonal latin squares. Each subject may get each tratment at most once. The design is a generalized Youden design that is also balanced for carryover effects.

### Usage

1 | ```
des.MOLS(trt, k = trt)
``` |

### Arguments

`trt` |
A prime power less than 100. The number of treatments (products) to be tested. |

`k` |
An integer |

### Details

A complete set of mutually orthogonal latin squares is constructed using Galois Fields.
The rows of the designs represent the treatment
orders for the subjects. If an incomplete design with *k* columns is needed,
only the first *k* columns of the designs are
considered.
The treatments are numbered 1,...,*trt*. The entry *(i,j)*
of the design corresponds to the treatment the *i*-th subject gets in the *j*-th period.

### Value

A matrix with *trt(trt-1)* rows and *k* columns representing the experimental design.

### Author(s)

Oliver Sailer

### References

Wakeling, I.N. and MacFie, H.J.H. (1995): Designing consumer trials balanced for first and higher orders of carry-over effect when only a subset of k samples from t may be tested. Food Quality and Preference 6, 299-308.

Williams, E. J. (1949): Experimental designs balanced for the estimation of residual effects of treatments. Australian Journal of Scientific Research, Ser. A 2, 149-168.

### See Also

`get.plan`

, `MOLS`

### Examples

1 2 |