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Combinatorics by Peter J. Cameron

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16. Designs

Though the uncarved block is smallNo one in the world dare claim its allegiance.

Lao Tse, Tao Te Ching (ca. 500 BC)

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TOPICS: Designs

TECHNIQUES: Matrix and determinant techniques; Cauchy’s Inequality (the ‘variance trick’)

ALGORITHMS:

CROSS-REFERENCES: Steiner triple systems (Chapter 8), finite geometries (Chapter 9), regular families (Chapter 7), PIE (Chapter 5), Latin squares, [SDRs] (Chapter 6)

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Designs are a generalisation of Steiner triple systems. There is no hope of deciding the values of the parameters for which designs exist ...

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