PGM2-package: PGM2: Recursive Construction of Nested Resolvable Designs and...

In PGM2: Recursive Construction of Nested Resolvable Designs and Associated Uniform Designs

PGM2: Recursive Construction of Nested Resolvable Designs and Associated Uniform Designs

Description

Implements recursive construction methods for balanced incomplete block designs (BIBDs), their second generation, resolvable BIBDs (RBIBDs), and uniform designs (UDs) derived from projective geometries over GF(2). It enables extraction of nested structures in multiple stages and supports recursive resolution processes, as introduced in Boudraa et al. (2013).

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.

See Also

Useful links:

• https://mlaib.net

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)

PGM2 documentation built on June 9, 2025, 9:08 a.m.