PGM2 (version 1.0-1)

PGM2-package: Nested Resolvable Designs and their Associated Uniform Designs

Description

Construction method of nested resolvable designs from a projective geometry defined on Galois field of order 2. The obtained Resolvable designs are used to build uniform design. The presented results are based on and A. Boudraa et al. (See references).

References

D. Dugué Traité de statistique théorique et appliquée, Masson et Cie, 1958.

Gheribi-Aoulmi. Z and M. Bousseboua Recursive methods for construction of balanced n-ary block designs. Serdica Math.J (31), 2005,189-200

Fang.K.T et al., Constructions of uniform designs by using resolvable packings and coverings. Discrete Math. (19), 2003, 692-711.

Abla Boudraa, Zebida Gheribi-Aoulmi and Mohamed Laib. Recursive method for construction of nested resolvable designs and uniform designs associated. International Journal of Research and Reviews in Applied Sciences. Vol. 17, Issue 2 (2013).

Fang.K.T et al., Construction of uniform designs via super-simple resolvable t-designs. Util. Math. (66).2004, 15-32.

Examples

m<-4
X<-BIB(m)
n<-1
mat<-X$BIB
Y<-Resolvable(n,mat)   #Extract the RBIB
n<-1
mat<-X$BIB
X2<-Gen(n,mat)  #Extract the BIBD of the second generation
## Not run: 
# #Algorithm of the 3rd example in the paper : (Abla Boudraa & al) IJRRAS.
# #(17), Issue 2 (2013).
# 
# bib<-BIB(3)$BIB
# mat<-NULL
# for(i in 1:15){mat[[i]]<-Gen(i,bib)$BIB2}
# x<-Reduce("rbind",mat)
# e<-dim(x)[1]
# b<-dim(x)[2]
# v<-bib[1,]
# for (i in 1:e) {for (j in 1:b) {if (any (x[i,j]==v)) {x[i,j]<-0}}}
# for (i in e:1) { if (all (x[i,]==0)) {x<-x[-i,]}}
# s<-x[1,]
# s<-s[s>0]
# h<-length(s)
# f<-dim(x)[1]
# x1<-matrix(nrow=f, ncol=h)
# for (i in 1:f) {x1[i,]<-x[i,][x[i,]>0]}
# A<-unique(x1)
# UD<-Uniform(A)
# ## End(Not run)