Gen: BIBD of the Next Generation

In PGM2: Recursive Construction of Nested Resolvable Designs and Associated Uniform Designs over GF(p)

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)

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.

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.

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.

Author(s)

Mohamed Laib, Abla Boudraa and Zebida Gheribi-Aoulmi

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

PGM2 documentation built on Aug. 27, 2026, 9:07 a.m.