GraecoLatin {blocksdesign}

Graeco-Latin squares

Description

Constructs mutually orthogonal Graeco-Latin squares for the following N:

i) any odd valued N

ii) any prime-power N = p**q where p and q can be chosen from

prime p	maximum q
2	13
3	8
5	6
7	5
11	4
13 17 19 23	3
29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97	2
Any prime >97	1

iii) any even valued N <= 30 except for 6 or 2

Usage

GraecoLatin(N)

Arguments

N

any suitable integer N

Details

Plans are given for pairs of MOLS classified by rows and columns. The output is a single data frame of size p**q x (r+2) for the required set of MOLS with a column for the rows classification, a column for the columns classification and a column for each treatment set from the required set of MOLS.

Also see the function MOLS which will generate complete sets of MOLS for prime-power design sizes.

Value

Data frame of factor levels for rows, columns and treatment sets

References

Street, A. P. & Street, D. J. (1987). Combinatorics of Experimental Design, Chapters 6 and 7. Clarendon Press, Oxford.

See Also

MOLS

Examples

X=GraecoLatin(8) 
table(X[,3],X[,4])
X=GraecoLatin(9) 
table(X[,3],X[,4])
X=GraecoLatin(32)
table(X[,3],X[,4])