✦ LIBER ✦

On Steiner 3-wise balanced designs of order 17

✍ Scribed by E. S. Kramer; D. L. Kreher; Rudolf Mathon

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 231 KB
Volume: 5
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1997)5:2<125::aid-jcd4>3.0.co;2-h

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✦ Synopsis

We determine all S(3, K, 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, K, 16) which is not an S(3, 4, 16). There is an S(3, K, 17) with |G| = n if and only if n ∈ {2 a 3 b : 0 ≤ a ≤ 7, 0 ≤ b ≤ 1} ∪ {18, 60, 144, 288, 320, 1920, 5760, 16320}. We also search the S(3, K, 17)'s listed in the appendix for subdesigns S(2, K, 17) and generate 22 nonisomorphic S(3, K, 18)'s by adding a new point to such a subdesign.

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