Abstract
In this study, we propose a new method of construction of rectangular Partially Balanced Incomplete Block (PBIB) designs of size k = 2s and 2≤s < l and singular Group Divisible (GD) designs of size k = 2l, l is the number of columns in a rectangular matrix containing v = n × l treatments. We give the parameters expression of the obtained designs. Furthermore, we provide two algorithms of calculation for practical use.
Highlights
INTRODUCTIONA Group Divisible (GD) design is a 2-associated Partially Balanced Incomplete Block (PBIB) design based on a group divisible association
A Group Divisible (GD) design is a 2-associated Partially Balanced Incomplete Block (PBIB) design based on a group divisible associationA PBIB designs, based on an m-association scheme, with parameters v, b, r, k, _i, i = 1,2,3...m, is a block design with v treatments and b blocks of size k each such that every treatment occurs in r blocks and any two distinct treatments being ith associate occur together in exactly λi blocks
We propose a new method of construction of rectangular Partially Balanced Incomplete Block (PBIB) designs of size k = 2s and 2 ≤ s < l and singular Group Divisible (GD) designs of size k = 2l, l is the number of columns in a rectangular matrix containing v = n × l treatments
Summary
A Group Divisible (GD) design is a 2-associated PBIB design based on a group divisible association. The experimental rectangular designs are important subclasses of partially balanced block designs They were introduced for the first time by (Vartak, 1955), since several construction methods have been vr = bk. Rectangular designs, introduced by (Vartak, 1955), are 3-associated PBIB designs based on rectangular association scheme of v = n×l treatments arranged in. Let v = nl treatments arranged in an array of n rows and l columns as follows: Corresponding Author: Rezgui Imane, Department of Mathematics, University Constantine 1, Algeria. Let v = 12 = 3.4, (n = 3 and l = 4) treatments arranged in the following array: Applying the combinatory method (s), s = 2 we obtain the following rectangular design with parameters:
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