ym2 {PBIBD} | R Documentation |
Constructs Youden-m square designs and provides the parameters of the corresponding PBIB design
Description
By omitting the middle 2t
rows (where t = 1, 2, \ldots
) from any even-ordered Circulant matrix with order v \geq 6
, and considering only those rows that lie either above or below the omitted 2t
rows, the resulting arrangement gives a new type of Youden-m square.
The columns of these Youden-m squares constitute m
-associate class PBIB designs, with the following parameters:
-
v \geq 6
and even,b = v
,r = k = \frac{v}{2} - t
-
\lambda_1 = r - 2
,\lambda_m = \lambda_1 + 1
If
m
is even, then:-
\lambda_{i+1} = \lambda_i - 2
fori = 1, 2, \ldots, \frac{m}{2}
-
\lambda_{i-1} = \lambda_i - 2
fori = m, m-1, \ldots, \frac{m}{2} + 1
-
If
m
is odd, then:-
\lambda_{i+1} = \lambda_i - 2
fori = 1, 2, \ldots, \frac{m+1}{2}
-
\lambda_{i-1} = \lambda_i - 2
fori = m, m-1, \ldots, \left(\frac{m+1}{2}\right) + 1
-
Usage
ym2(n, t)
Arguments
n |
|
t |
|
Value
The function returns the required Youden-m square design and the parameters of the PBIB design constituted by taking the incomplete columns of the Youden-m square as blocks.
Author(s)
Kush Sharma, Davinder Kumar Garg
Examples
ym2(8, 1)