Title

On steiner 3-wise balanced designs of order 17

Document Type

Article

Publication Date

1-1-1997

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. © 1997 John Wiley & Sons, Inc.

Publication Title

Journal of Combinatorial Designs

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