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Type: Package
Title: Construction Methods for Series of PBIB Designs via Combinatory Method S
Version: 1.2
Date: 2025-05-27
Description: Provides constructions of series of partially balanced incomplete block designs (PBIB) based on the combinatory method S, introduced by Rezgui et al. (2014) <doi:10.3844/jmssp.2014.45.48>. This package also offers the associated U-type designs. Version 1.1-1 generalizes the approach to designs with v = wnl treatments. It includes various rectangular and generalized rectangular right angular association schemes with 4, 5, and 7 associated classes.
Imports: stats, utils
URL: https://mlaib.net
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.3.2
NeedsCompilation: no
Packaged: 2025-05-27 22:20:16 UTC; laib
Author: Mohamed Laib [aut, cre], Imane Rezgui [aut], Zebida Gheribi-Aoulmi [aut], Herve Monod [aut]
Maintainer: Mohamed Laib <laib.med@gmail.com>
Repository: CRAN
Date/Publication: 2025-05-27 23:00:27 UTC

The Combinatory Method (s) for the construction of rectangular PBIB designs

Description

The application of the Combinatory Method (s), with s chosen in [2, l-1], on rectangular association scheme to obtain the configuration and the parameters of the PBIB design associated.

Usage

CombS(n, l, s)

Arguments

n

Number of lines of the association schemes array.

l

Number of columns of the association schemes array.

s

Number of the token treatments from the same row of the association scheme.

Details

Value

A LIST :

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi (2014). New construction method of rectangular partially balanced incomplete block designs and singular group divisible designs, Journal of Mathematics and Statistics, 10, 45- 48.

M.N. Vartak 1955. On an application of Kronecker product of Matrices to Statistical designs. Ann. Math. Stat.,26(420-438).

See Also

UType

Examples

## Not run: 
n<-3
l<-3
s<-2
CombS(l,n,s)

## End(Not run)

Generalized rectangular right angular (4) design with \lambda_4 = 0

Description

Gives the configuration and the parametres of the design obtained by the first construction method of GPBIB_4 (see 3.1.1 of the paper rezgui et al (2015)).

Usage

GPBIB4A(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.

l

Number of columns of the association schemes array.

s

Number of the token treatments from the same row of the association scheme.

w

Number of the association scheme arrays.

Details

Value

A LIST :

Note

For w=2, the GPBIB_4 is a rectangular right angular (4) (PBIB_4)

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, doi:10.4236/am.2015.62024, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB4B and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB4A(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (4) design with \lambda_4 not equal to 0

Description

Gives the configuration and the parametres of the design obtained by the seconde construction method of GPBIB_4 (see 3.1.2 of the paper rezgui et al (2015)).

Usage

GPBIB4B(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.

l

Number of columns of the association schemes array.

s

Number of the token treatments from the same row of the association scheme.

w

Number of the association scheme arrays.

Value

A LIST :

Note

For w=2, the GPBIB_4 is a rectangular right angular (4) (PBIB_4)

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, doi:10.4236/am.2015.62024, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB4A and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB4B(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (5) design.

Description

gives the configuration and the parametres of the design obtained by the construction method of GPBIB_5 (see 3.2 of the paper rezgui et al (2015)).

Usage

GPBIB5(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.

l

Number of columns of the association schemes array.

s

Number of the token treatments from the same row of the association scheme.

w

Number of the association scheme arrays.

Value

A LIST :

Note

For w=2, the GPBIB_5 is a rectangular right angular (5) (PBIB_5).

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, doi:10.4236/am.2015.62024, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB5(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (7) design with \lambda_{i} equal to \lambda_{i+4} (i=1,...,4)

Description

gives the configuration and the parametres of the design obtained by the first construction method of GPBIB_7 (see 3.3.1 of the paper rezgui et al (2015))

Usage

GPBIB7A(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.

l

Number of columns of the association schemes array.

s

Number of the token treatments from the same row of the association scheme.

w

Number of the association scheme arrays.

Value

A LIST :

Note

For w=2, the GPBIB_7 is a rectangular right angular (7) (PBIB_7).

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, doi:10.4236/am.2015.62024, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB7B and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB7A(n, l, s, w)

## End(Not run)

Generalized rectangular right angular (7) design with distinct \lambda_i (i=1,...,7)

Description

Gives the configuration and the parametres of the design obtained by the seconde construction method of GPBIB_7 (see 3.3.2 of the paper rezgui et al (2015)).

Usage

GPBIB7B(n, l, s, w)

Arguments

n

Number of lines of the association schemes array.

l

Number of columns of the association schemes array.

s

Number of the token treatments from the same row of the association scheme.

w

Number of the association scheme arrays.

Value

A LIST :

Note

For w=2, the GPBIB_7 is a rectangular right angular (7) (PBIB_7).

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

Imane Rezgui, Z. Gheribi-Aoulmi and H. Monod (2015). U-type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes, doi:10.4236/am.2015.62024, Applied mathematics, 6, 242-264.

Imane Rezgui, Z.Gheribi-Aoulmi and H. Monod, New association schemes with 4, 5 and 7 associated classes and their associated partially balanced incomplete block designs; Advances and Applications in Discrete Mathematics Vol.12 Issue 2 197-206.

See Also

GPBIB7A and UType

Examples

## Not run: 
n<-3
l<-3
s<-3
w<-3
GPBIB7B(n, l, s, w)

## End(Not run)

U-type design via some PBIB designs

Description

Applies the Fang algorithm on our constructed designs to obtain the configuration and the parameters of the U-type design associated.

Usage

UType(lst)

Arguments

lst

The output of one of our package functions.

Value

A LIST :

Author(s)

Mohamed Laib, Imane Rezgui, Zebida Gheribi-Aoulmi and Herve Monod

References

K.T. Fang, R.Li and A.Sudjanto (2006). Design ans Modeling for Computer Experiments. Taylor & Francis Group, LLC London.

Examples

## Not run: 
M<-GPBIB4A(4,4,2,2)
UType(M)

## End(Not run)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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