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Encyclopaedia of DesignTheory:
A square design
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Consider the following eleven blocks (subsets of {1,2,...,11}):
- {1,3,4,5,9}
- {2,4,5,6,10}
- {3,5,6,7,11}
- {4,6,7,8,1}
- {5,7,8,9,2}
- {6,8,9,10,3}
- {7,9,10,11,4}
- {8,10,11,1,5}
- {9,11,1,2,6}
- {10,1,2,3,7}
- {11,2,3,4,8}
They have the following properties:
- there are eleven points and five blocks;
- any block contains five points, and any point lies in five blocks;
- any two blocks meet in two points, and any two points lie in two blocks.
So these blocks form a 2-(11,5,2) design.
Other examples of square designs can be found here under
"polarity" and "Youden
square".
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Peter J. Cameron
4 October 2002