## Combinatorial designs: construction methods |

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### Contents

Table of contents | 9 |

Introduction to basics | 15 |

Difference methods | 49 |

Copyright | |

13 other sections not shown

### Common terms and phrases

affine plane array BIBD block designs blocks containing codewords combinatorial designs Consider Corollary corresponding cyclic dealt defined Definition denote design exists difference set disjoint element occurs elements of G entry exactly once Example Exercises finite fields finite projective plane GF(q gives Hadamard designs Hadamard matrix hyperplanes idempotent incidence matrix integer Kirkman triple systems league schedule LEMMA matrix of order mixed difference system mod 2m MOLS of order multiplier non-zero elements Note number of blocks obtain order 2n order n exists pair of elements plane of order player precisely prime power primitive element Proof Let proof of Theorem replace resolution class resolvable result round row and column rows of G SAMDRR(n Show SOLS SOLS(n square of order starter Steiner system Steiner triple system STS(u Suppose symmetric design symmetric v,k,X system of order transversal designs unique block whist tournaments Wilson's theorem yields