Package 'CombinS' reference manual

Title:	Construction Methods for Series of PBIB Designs via Combinatory Method S
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.
Authors:	Mohamed Laib [aut, cre], Imane Rezgui [aut], Zebida Gheribi-Aoulmi [aut], Herve Monod [aut]
Maintainer:	Mohamed Laib <[email protected]>
License:	GPL-3
Version:	1.2
Built:	2026-05-26 08:38:44 UTC
Source:	https://github.com/mlaib/combins

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)
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

For $2 < s < l$ , we obtain a rectangular PBIB design.
For $s = l$ , we obtain a singular group divisible designs.

Value

A LIST :

PBIB The configuration of the PBIB.
Type The type of the design
V Number of treatments.
B Number of blocs.
R Repetition of each treatment.
K Size of blocs.
lamda Vector of m-lambda.
Resolvable Is the design Resolvable ?

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).

Examples

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

## End(Not run)
## 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)
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

For $s = l$ , the previous method gives configuration of nested group divisible designs.

Value

A LIST :

PBIB The configuration of the PBIB.
Type The type of the design
V Number of treatments.
B Number of blocs.
R Repetition of each treatment.
K Size of blocs.
lamda Vector of m-lambda.
Resolvable Is the design Resolvable ?

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.

Examples

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

## End(Not run)
## 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)
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 :

PBIB The configuration of the PBIB.
Type The type of the design
V Number of treatments.
B Number of blocs.
R Repetition of each treatment.
K Size of blocs.
lamda Vector of m-lambda.
Resolvable Is the design Resolvable ?

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

Examples

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

## End(Not run)
## 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)
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 :

PBIB The configuration of the PBIB.
Type The type of the design
V Number of treatments.
B Number of blocs.
R Repetition of each treatment.
K Size of blocs.
lamda Vector of m-lambda.
Resolvable Is the design Resolvable ?

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

Examples

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

## End(Not run)
## 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)
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 :

PBIB The configuration of the PBIB.
Type The type of the design
V Number of treatments.
B Number of blocs.
R Repetition of each treatment.
K Size of blocs.
lambda Vector of m-lambda.
Resolvable Is the design Resolvable ?

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

Examples

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

## End(Not run)
## 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)
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 :

PBIB The configuration of the PBIB.
Type The type of the design
V Number of treatments.
B Number of blocs.
R Repetition of each treatment.
K Size of blocs.
lambda Vector of m-lambda.
Resolvable Is the design Resolvable ?

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

Examples

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

## End(Not run)
## 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)
UType(lst)

Arguments

lst

The output of one of our package functions.

Value

A LIST :

v Number of runs.
r Number of factors.
UtypeDesign The configuration of the U-type design..

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

## End(Not run)

Package 'CombinS'

Help Index

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

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Generalized rectangular right angular (4) design with λ4\lambda_4λ4​ = 0

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Generalized rectangular right angular (4) design with λ4\lambda_4λ4​ not equal to 0

Description

Usage

Arguments

Value

Note

Author(s)

References

See Also

Examples

Generalized rectangular right angular (5) design.

Description

Usage

Arguments

Value

Note

Author(s)

References

See Also

Examples

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

Description

Usage

Arguments

Value

Note

Author(s)

References

See Also

Examples

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

Description

Usage

Arguments

Value

Note

Author(s)

References

See Also

Examples

U-type design via some PBIB designs

Description

Usage

Arguments

Value

Author(s)

References

Examples

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

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

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

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