# Construction of Complete Sets of Mutually Orthogonal Latin Squares

### Description

The function constructs sets of mutually othogonal latin squares (MOLS) using Galois fields. The construction works for prime powers only.

### Usage

1 |

### Arguments

`p` |
A prime number less than 100. |

`n` |
A positive integer. |

`primpol` |
A primitive polynomial of the Galois Field GF( |

### Details

If *trt = p^n* is a prime power, then *trt*-1 latin squares of order *trt*
are constructed.
The elements of the squares are numbered 1,...,*trt*.
These squares are mutually orthogonal, i.e. if any two of them are superimposed, the resulting
array will contain each ordered pair *(i,j)*, *i*,*j* in {1,...,
*trt*} exactly once.
The squares are in standard order, i.e. the first row is always equal to (1,...,*trt*).
A primitive polynomial may be constructed automatically using the internal function `GF`

.

### Value

For *trt = p^n*, an array that contains *trt*-1 latin squares is returned.

### Author(s)

Oliver Sailer

### References

Cherowitzo, W.: http://www-math.cudenver.edu/~wcherowi/courses/finflds.html

Street, A.P. and Street, D.J. (1987): Combinatorics of experimental design. Oxford University Press, Oxford.

### See Also

`des.MOLS`

### Examples

1 2 |