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A construction for Steiner 3-designs

Blanchard, John L. (1995) A construction for Steiner 3-designs. Journal of Combinatorial Theory. Series A, 71 (1). pp. 60-66. ISSN 0097-3165. doi:10.1016/0097-3165(95)90015-2.

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Let q be a prime power. For every ν satisfying necessary arithmetic conditions we construct a Steiner 3-design S(3, q + 1; ν · q^n + 1) for every n sufficiently large. Starting with a Steiner 2-design S(2, q; ν), this is extended to a 3-design S_λ(3, q + 1; ν + 1), with index λ = q^d for some d, such that the derived design is λ copies of the Steiner 2-design. The 3-design is used, by a generalization of a construction of Wilson, to form a group-divisible 3-design GD(3, {q, q + 1}, νp^d) with index one. The structure of the derived design allows a circle geometry S(3, q + 1; q^d + 1) to be combined with the group-divisible design to form, via a method of Hanani, the desired Steiner 3-design S(3, q + 1; νq^n + 1), for all n ⩾ n_0.

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Additional Information:© 1995 Academic Press, Inc. Received 12 May 1994. Communicated by the Managing Editors.
Issue or Number:1
Record Number:CaltechAUTHORS:20170906-094100269
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Official Citation:John L Blanchard, A construction for Steiner 3-designs, Journal of Combinatorial Theory, Series A, Volume 71, Issue 1, 1995, Pages 60-66, ISSN 0097-3165, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81183
Deposited By: Ruth Sustaita
Deposited On:06 Sep 2017 17:09
Last Modified:15 Nov 2021 19:41

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