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An inequality for steiner systems II

โœ Scribed by Ryuzaburo Noda

Publisher
Springer Japan
Year
1996
Tongue
English
Weight
187 KB
Volume
12
Category
Article
ISSN
0911-0119

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Given a Steiner system S(2,k-1;v) with v>~vo(k), there is a 3-design Sa(3, k;v+ t) such that the derived design is 2 copies of the Steiner system for any 2 sufficiently large satisfying the standard arithmetic conditions. This theorem has applications in the construction of Steiner 3-designs.

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## An automorphism group of a nontrivial (possibly infinite) Steiner triple system has at least as many block-orbits as point-orbits. The proof is a translation of that in the finite case, with a small twist. For block size 4, the argument fails, and, indeed, the stronger statement (involving blo