blocksdesign (version 3.6)

MOLS: Prime power MOLS from finite fields

Description

Finds MOLS for r squares of dimension p**q where r < p**q and p is prime and either q is 1 for any p or q < 13 for p = 2, or q < 8 for p = 3, or q < 6 for p = 5, or q < 5 for p = 7, or q < 4 for p = 11, 13, 17 or 19 or q < 3 for any other prime <100.

Usage

MOLS(p, q, r)

Arguments

p

is a prime (see description)

q

is an integer power (see description)

r

is the total number of replicates < p**q

Value

dataframe of factor levels for rows, columns and treatmnent sets

Details

Finds MOLS by cyclic permuation of the elements of a prime number or the elements of a prime-power finite field based on a suitable choice of primitive polynomial. Primitive polynomials for the sizes of finite fields outlined in the description are extracted from the Supplement to Hansen and Mullen (1992)

References

HANSEN, T. & MULLEN, G. L. (1992) PRIMITIVE PolynomF::polynomialS OVER FINITE FIELDS Mathematics of Computation, 59, 639-643 and Supplement.

Examples

# NOT RUN {
MOLS(2,3,7)
MOLS(3,2,4)
# }
# NOT RUN {
MOLS(3,3,4)
# }
# NOT RUN {
 
# }
# NOT RUN {
MOLS(23,2,2)
# }
# NOT RUN {
 
# }