| Summary: | Thesis (M.Sc.)--Memorial University of Newfoundland, 2008. Mathematics and Statistics Includes bibliographical references (leaves 89-94) A packing design , or a PD(v, k , λ) is a family of k -subsets (called blocks), of a v -set S , such that every 2-subset (called a pair ), of S is contained in at most λ blocks. The packing number P(v, k , λ) is the number of blocks in a PD(v, k , λ). -- The edges in the multigraph λKv not contained in the packing form the leave of the PD( v, k , λ), denoted by leave(v, k , λ). Generally we consider maximum packings (packings with maximum number of blocks) unless stated otherwise. -- A covering design , or a CD(v, k , λ) is a family of k -subsets (called blocks ), of a v -set S , such that every 2-subset (called a pair ), of S is contained in at least λ blocks. The covering number C(v, k , λ) is the number of blocks in a CD(v, k , λ). -- The extrone edges added to the multigraph λKv in the covering form the excess of the CD(v, k , λ), denoted by excess(v, k , λ). Generally we consider minimum coverings (coverings with minimum number of blocks) unless stated otherwise. -- In this thesis we give the direct constructions of the leaves and excesses for k = 3, 4. Some of them are from existing papers, some are the author's original work. This is the first time to put all the leaves and excesses for k = 4 and all λs together (with only few possible exceptions).
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