## Combinatorial Designs: A Tribute to Haim HananiHaim Hanani pioneered the techniques for constructing designs and the theory of pairwise balanced designs, leading directly to Wilson's Existence Theorem. He also led the way in the study of resolvable designs, covering and packing problems, latin squares, 3-designs and other combinatorial configurations. The Hanani volume is a collection of research and survey papers at the forefront of research in combinatorial design theory, including Professor Hanani's own latest work on Balanced Incomplete Block Designs. Other areas covered include Steiner systems, finite geometries, quasigroups, and t-designs. |

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### Contents

1 | |

5 | |

21 | |

29 | |

Chapter 4 New cyclic 61 244 40 10 6 BIBDs Note | 51 |

Chapter 5 A unital in the Hughes plane of order nine Note | 55 |

Chapter 6 Percentages in pairwise balanced designs | 57 |

Chapter 7 On complete arcs in Steiner systems S2 3v and S2 4v | 65 |

Chapter 16 On the 15 5 λfamily of BIBDs | 205 |

Chapter 17 Finite bases for some PBDclosed sets | 217 |

Chapter 18 On the constructive enumeration of packings and coverings of index one | 237 |

Chapter 19 The existence of simple S33 4 v | 255 |

Chapter 20 On combinatorial designs with subdesigns | 259 |

Chapter 21 Cyclical Steiner Triple Systems orthogonal to their opposites | 281 |

Chapter 22 Symmetric quasigroups of odd order | 285 |

Chapter 23 Partitioning sets of quadruples into designs I | 299 |

Chapter 8 A survey of recent works with respect to a characterization of an n k d qcode meeting the Griesmer bound using a minhyper in a finite pro... | 75 |

Chapter 9 BIBDs with blocksize seven | 89 |

Chapter 10 On Alspachs conjecture | 97 |

Chapter 11 Some selfblocking block designs | 123 |

Chapter 12 The Steiner systems S 2 4 25 with nontrivial automorphism group | 137 |

Chapter 13 Balanced tournament designs and related topics | 159 |

Chapter 14 Automorphisms of 222 8 4 designs | 177 |

Chapter 15 Nesting of cycle systems of odd length | 191 |

Chapter 24 Infinite families of strictly cyclic Steiner quadruple systems | 307 |

Chapter 25 Minimal pairwise balanced designs | 317 |

Chapter 26 Combinatorial problems in repeated measurements designs | 323 |

Chapter 27 Locally trivial tdesigns and tdesigns without repeated blocks | 345 |

Chapter 28 A new family of BIBDs and nonembeddable 16 24 9 6 3designs | 357 |

Chapter 29 Modifications of the centralmethod to construct Steiner triple systems | 367 |

Author Index to Volume 77 | 385 |

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### Common terms and phrases

1-factor array automorphism group automorphism of order Baer subplane balanced incomplete block balanced tournament designs BIBD block designs block size blocking set column combinatorial combinatorial designs complete graph construction contains Corollary cyclic deﬁned Deﬁnition denote Discrete Math disjoint edges elements ex-points exactly exists Fano Planes ﬁnite ﬁrst ﬁxed blocks ﬁxed points form B[7 frame of type frame resolvable GD[k graph group divisible design Hamada Hanani idempotent incomplete block designs inﬁnite integers isomorphic Kirkman Kirkman triple systems Lamken Lemma m-cycle system Mendelsohn modulo non-isomorphic obtain orthogonal Latin squares oval pair pairwise balanced design parallel classes partition PG(t plane of order positive integers projective plane Proof Proposition quasigroup quasigroup satisfying resolution class resolvable GD[3 resolvable group divisible result satisﬁes secants skew frame squodd Steiner systems Steiner triple systems STS(v Table tactical decompositions tangents Theorem Theory uniform RMD vertex vertices