PGM2-package {PGM2}

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 <https://eudml.org/doc/219563> and A. Boudraa et al. (See references).

Note

This work established in same time with the article intitled: Abla Boudraa et al., Recursive method for construction of nested resolvable designs and uniform designs associated, International Journal of Research and Reviews in Applied Sciences, (17), Issue 2 (2013).

Author(s)

Mohamed Laib, Abla Boudraa and Zebida Gheribi-Aoulmi

Maintainer: Mohamed Laib [e-mail]

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)