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Designs, Codes and Cryptography

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04-02-2020

On the number of resolvable Steiner triple systems of small 3-rank

Authors: Minjia Shi, Li Xu, Denis S. Krotov

Published in: Designs, Codes and Cryptography | Issue 6/2020

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Abstract

In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order v, where \(v=3^k\), and 3-rank \(v-k\). We develop an approach to generalize this bound and estimate the number of isomorphism classes of resolvable STS (v) of 3-rank \(v-k-1\) for an arbitrary v of form \(3^kT\), where T is congruent to 1 or 3 modulo 6.

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Title: On the number of resolvable Steiner triple systems of small 3-rank
Authors: Minjia Shi
Li Xu
Denis S. Krotov
Publication date: 04-02-2020
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 6/2020
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-020-00725-y

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