# PGM2: Recursive Construction of Nested Resolvable Designs and Associated Uniform Designs 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). package ## 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). ## Examples ```r 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) ``` ## 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](https://mlaib.net) ## Author(s) Mohamed Laib, Abla Boudraa and Zebida Gheribi-Aoulmi Maintainer: Mohamed Laib laib.med@gmail.com

PGM2-package