On steiner 3-wise balanced designs of order 17
Document Type
Article
Publication Date
1997
Department
Department of Mathematical Sciences
Abstract
We determine all S(3, κ, 17)'s which either; (i) have a block of size at least 6; or (ii) have an automorphism group order divisible by 17, 5, or 3; or (iii) contain a semi-biplane; or (iv) come from an S(3, κ, 16) which is not an S(3, 4, 16). There is an S(3, κ, 17) with |G| = n if and only if n ∈ {2a3b: 0 ≤ a ≤ 7, 0 ≤ b ≤ 1} ∪ {18, 60, 144, 288, 320, 1920, 5760, 16320}. We also search the S(3, κ, 17)'s listed in the appendix for subdesigns S(2, κ, 17) and generate 22 nonisomorphic S(3, κ, 18)'s by adding a new point to such a subdesign.
Publication Title
Journal of Combinatorial Designs
Recommended Citation
Kramer, E.,
Kreher, D. L.,
&
Mathon, R.
(1997).
On steiner 3-wise balanced designs of order 17.
Journal of Combinatorial Designs,
5(2), 125-145.
http://doi.org/10.1002/(SICI)1520-6610(1997)5:2<125::AID-JCD4>3.0.CO;2-H
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