ym2 {PBIBD}

The function constructs Youden-m square designs. The function provides the parameters of the PBIB design constituted when the incomplete columns of this Youden-m square are taken as blocks.

Description

By omitting the middle 2t (t = 1, 2, ...) rows of any even ordered Circulant matrix with order v >= 6 and considering only those rows which lie either above or below the omitted 2t rows, the resulting arrangement of rows 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 >= 6 and even, b = v, r = k = (v/2)-t, lambda 1 = r-2, lambda m = lambda 1+1

If m is even, then lambda i+1 = lambda i - 2; i = 1, 2, ..., m/2 and lambda i-1 = lambda i - 2; i = m, m-1, ..., (m/2)+1

If m is odd, then lambda i+1 = lambda i - 2; i = 1, 2, ..., (m+1)/2 and lambda i-1 = lambda i - 2; i = m, m-1, ..., ((m+1)/2) + 1

Usage

ym2(n, t)

Arguments

n

n is the order of the circulant matrix which is also the number of treatments

t

t is the number of rows you want to omit from both ends of the circulant matrix

Value

The function returns the required Youden-m square design. It also returns 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)