crossdes (version 1.1-2)

MOLS: 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

MOLS(p, n, primpol = GF(p, n)[[2]][1, ])

Arguments

p

A prime number less than 100.

n

A positive integer.

primpol

A primitive polynomial of the Galois Field GF(\(p^n\)).

Value

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

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.

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

# NOT RUN {
MOLS(7,1) # 6 mutually orthogonal latin squares of order 7
MOLS(2,3) # 7 mutually orthogonal latin squares of order 8
# }