PGM2 (version 2.0.1)

Gen: BIBD of the Next Generation

Description

Extracts the balanced incomplete block design of the next generation by deleting block n of a BIBD built from a projective geometry: each remaining block is intersected with the deleted one, so the deleted block plays the role of a lower-dimensional projective geometry and the intersections are its hyperplanes.

Usage

Gen(n, mat)

Value

A list with components:

V

Number of treatments of the new BIBD.

B

Number of blocks.

R

Replication of each treatment.

K

Size of each block.

BIB2

The design: a matrix whose rows are the blocks.

Arguments

n

Index of the block (sub-variety) to be deleted; an integer between 1 and nrow(mat).

mat

The matrix of the BIBD (rows are blocks), e.g. the BIB component returned by BIB.

Author

Mohamed Laib, Abla Boudraa and Zebida Gheribi-Aoulmi

Details

Works for any order p: block sizes are derived from the data instead of the binary-only formula used in PGM2 <= 1.2 (for a symmetric BIBD every remaining block meets the deleted block in exactly Lambda treatments). For a BIBD from PG(m, p), the result is the BIBD of PG(m - 1, p) on the treatments of the deleted block.

References

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.

Examples

X <- BIB(4)              # BIBD (31, 15, 7) from PG(4, 2)
X2 <- Gen(1, X$BIB)      # second generation: BIBD (15, 7, 3)
X2$V; X2$K

Y <- BIB(3, p = 3)       # BIBD (40, 13, 4) from PG(3, 3)
Y2 <- Gen(1, Y$BIB)      # second generation: BIBD (13, 4, 1)
Y2$V; Y2$K