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Encyclopaedia of DesignTheory: A Youden "square"

Youden represented his designs as Latin rectangles; Fisher represented them as partial Latin squares. The entry in the ith row and jth column of Fisher's square is k if and only if the entry in the kth row and ith column of Youden's rectangle is j.

A Youden square is based on a square 2-design D. Each row of Youden's rectangle is a permutation of the numbers 1,2,...,n, while the columns are the blocks of D. If the blank and non-blank entries of Fisher's square are replaced by 0 and 1 respectively, we obtain the incidence matrix of D.

Here is an example, where the design is a 2-(7,3,1).

Youden's representation:

1	2	3	4	5	6	7
2	3	4	5	6	7	1
4	5	6	7	1	2	3

Fisher's representation:

1	2		3
	1	2		3
		1	2		3
			1	2		3
3				1	2
	3				1	2
2		3				1

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Peter J. Cameron
4 October 2002