
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 2design 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 nonblank 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).
1  2  3  4  5  6  7 
2  3  4  5  6  7  1 
4  5  6  7  1  2  3 
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