PGM2 (version 2.0.1)

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

Description

Recursive construction of balanced incomplete block designs (BIBDs), their successive generations, resolvable BIBDs (RBIBDs) and associated uniform designs (UDs), derived from finite projective geometries PG(m, p) over a Galois field GF(p) of any prime order p.

Version 2.0 generalises the whole package from GF(2) to GF(p) for any prime p, as described in the underlying paper (Boudraa et al., 2013), whose theory is stated for general p even though versions <= 1.2 of the package implemented only p = 2.

Author

Maintainer: Mohamed Laib

Authors:

• Mohamed Laib

• Abla Boudraa

• 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.

D. Dugue (1958). Traite de statistique theorique et appliquee. Masson et Cie, Paris.

Z. Gheribi-Aoulmi and M. Bousseboua (2005). Recursive methods for construction of balanced n-ary block designs. Serdica Mathematical Journal, 31, 189--200.

K.T. Fang, X. Lu, Y. Tang and J. Yin (2004). Constructions of uniform designs by using resolvable packings and coverings. Discrete Mathematics, 274, 25--40.

K.T. Fang, G.N. Ge, M.Q. Liu and H. Qin (2004). Construction of uniform designs via super-simple resolvable t-designs. Utilitas Mathematica, 66, 15--32.

See Also

Useful links:

• https://mlaib.net

• https://github.com/mlaib/PGM2

• Report bugs at https://github.com/mlaib/PGM2/issues

Examples

# The chain of designs of PG(3, 2):
X <- BIB(3)                  # BIBD (15, 7, 3)
Y <- Resolvable(1, X$BIB)    # RBIBD (8, 14, 7, 4, 3)
Uniform(Y$RBIB)$UD           # U(8, 2^7)

# The same chain over GF(3):
X3 <- BIB(2, p = 3)          # BIBD (13, 4, 1)
Y3 <- Resolvable(1, X3$BIB)  # RBIBD (9, 12, 4, 3, 1)
Uniform(Y3$RBIB)$UD          # U(9, 3^4)