A finite embedding theorem for partial Steiner 3-designs

A Steiner system S(t,k,n) is a k-uniform set system on [n] for which every t-set is covered exactly once. More generally, a partial Steiner system P(t,k,n) is a k-uniform set system on [n] where every t-set is covered at most once. Let q be a prime power. Using circle geometries and field-based bloc...

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Bibliographic Details
Published in:Finite fields and their applications 2015-05, Vol.33, p.29-36
Main Authors: Dukes, Peter J., Feng, Tao, Ling, Alan C.H.
Format: Article
Language:English
Subjects:
3-Design
Circle geometry
Embedding
Steiner system
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Summary:A Steiner system S(t,k,n) is a k-uniform set system on [n] for which every t-set is covered exactly once. More generally, a partial Steiner system P(t,k,n) is a k-uniform set system on [n] where every t-set is covered at most once. Let q be a prime power. Using circle geometries and field-based block spreading, we give an explicit embedding for any partial Steiner system P(3,q+1,n) into a Steiner system S(3,q+1,qm+1) for some m=m(q,n).
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2014.09.011