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- Title
Some new large sets of geometric designs of type LS[3][2, 3, 2<sup>8</sup>].
- Authors
Hurley, Michael R.; Khadka, Bal K.; Magliveras, Spyros S.
- Abstract
Let V be an n-dimensional vector space over Fq. By a geometric t-[qn, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D: A large set, LS[N][t, k, qn], of geometric designs, is a collection of N t-[qn, k, λ] designs which partitions the collection ... of all k-dimensional subspaces of V . Prior to recent article [4] only large sets of geometric 1-designs were known to exist. However in [4] M. Braun, A. Kohnert, P. Östergard, and A. Wasserman constructed the world's first large set of geometric 2-designs, namely an LS[3][2,3,28], invariant under a Singer subgroup in GL8(2). In this work we construct an additional 9 distinct, large sets LS[3][2,3,28], with the help of lattice basis-reduction.
- Subjects
VECTOR spaces; SUBSPACES (Mathematics); SET theory; LATTICE theory; MATHEMATICAL analysis
- Publication
Journal of Algebra Combinatorics Discrete Structures & Applications, 2017, Vol 4, Issue 3, p165
- ISSN
2148-838X
- Publication type
Article
- DOI
10.13069/jacodesmath.40139