AM  Vol.6 No.2 , February 2015
U-Type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes
ABSTRACT
The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes (m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns (w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method (s). For n or l even and s divisor of n or l, the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U-type designs U (wnl;) (r is the repetition number of each treatment in our resolvable PBIB design).

Cite this paper
Rezgui, I. , Gheribi-Aoulmi, Z. and Monod, H. (2015) U-Type Designs via New Generalized Partially Balanced Incomplete Block Designs with m = 4, 5 and 7 Associated Classes. Applied Mathematics, 6, 242-264. doi: 10.4236/am.2015.62024.
References
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[5]   Rezgui, I. and Gheribi-Aoulmi, Z. (2014) New Construction Method of Rectangular PBIB Designs and Singular Group Divisible Designs. Journal of Mathematics and Statistics, 10, 45-48.
http://dx.doi.org/10.3844/jmssp.2014.45.48

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[8]   Rezgui, I., Gheribi-Aoulmi, Z. and Monod, H. (2013) New Association Schemes with 4, 5 and 7 Associate Classes and Their Associated Partially Balanced Incomplete Block Designs. Advances and Applications in Discrete Mathematics, 12, 207-215.

[9]   Laib, M., Rezgui, I., Gheribi-Aoulmi, Z. and Monod, H. (2013) Package “CombinS”: Constructions Method of Rectangular PBIB and Rectangular Right Angular PBIB(m) (m = 4, 5 and 7) Designs. Version 1.0.
http://cran.r-project.org/web/packages/CombinS/CombinS.pdf

 
 
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