Recursive construction of nested resolvable designs and their associated uniform designs from finite projective geometries PG(m, p) over a Galois field GF(p) of any prime order p.
The package implements and generalises the method of:
A. Boudraa, Z. Gheribi-Aoulmi and M. Laib (2013). Recursive method for construction of resolvable nested designs and uniform designs associated. International Journal of Research and Reviews in Applied Sciences, 17(2), 167–176.
The paper states its theory for any prime p; versions ≤ 1.2 of the package implemented only p = 2. Since version 2.0 the whole chain
PG(m, p) → BIB → next generations (Gen) → RBIB (Resolvable) → UD (Uniform)
works for every prime p, with results validated against the parameter tables of the paper (p = 2 and p = 3) by the test suite.
# from CRAN
install.packages("PGM2")
# development version
# remotes::install_github("mlaib/PGM2")
library(PGM2)
## Over GF(2) (identical to versions <= 1.2):
X <- BIB(4) # BIBD (31, 15, 7) from PG(4, 2)
Y <- Resolvable(1, X$BIB) # RBIBD (16, 30, 15, 8, 7)
Uniform(Y$RBIB)$UD # uniform design U(16, 2^15)
## Over GF(3):
X3 <- BIB(2, p = 3) # BIBD (13, 4, 1): projective plane of order 3
Y3 <- Resolvable(1, X3$BIB) # RBIBD (9, 12, 4, 3, 1): AG(2, 3)
Uniform(Y3$RBIB)$UD # uniform design U(9, 3^4)
## Every stage of the recursion at once:
s <- Steps(4, 1) # PG(4, 2): stages S1..S4
s3 <- Steps(3, 1, p = 3) # PG(3, 3)
See the vignette, vignette("PGM2-paper"), which reproduces the worked
examples of the 2013 paper together with the first-generation BIBD, RBIBD
and uniform-design rows of both of its parameter tables, and selected
reduced-design rows.
License: GPL-3
The paper-supplement/ directory (not part of the CRAN package) holds the
scripts, result files and archived designs behind the accompanying paper on
the projection spectrum and factor selection of these designs; see
paper-supplement/README.md. Releases are archived on Zenodo under the
concept DOI above.