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Published online by Cambridge University Press: 04 November 2009
Abstract
New algorithms are presented for finding spreads and packings of sets with applications to combinatorial designs and finite geometries. An efficient deterministic method for spread enumeration is used to settle several existence problems for t-designs and partial geometries. Randomized algorithms based on tabu search are employed to construct new Steiner 5-designs and large sets of combinatorial designs. In particular, partitions are found of the 4-subsets of a 16-set into 91 disjoint affine planes of order 4.
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