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

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).

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

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.

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

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.

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

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

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

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

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

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

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

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)