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More results on large sets of Kirkman triple systems

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Abstract

The existence of large sets of Kirkman triple systems (LKTSs) is one of the best-known open problems in combinatorial design theory. Steiner quadruple systems with resolvable derived designs (RDSQSs) play an important role in the recursive constructions of LKTSs. In this paper, we introduce a special combinatorial structure \(\hbox {RDSQS}^{*}(v)\) and use it to present a construction for RDSQS(4v). As a consequence, some new infinite families of LKTSs are given.

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Funding

Supported by NSFC Grant 11771119.

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Authors and Affiliations

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China

    Yan Liu & Jianguo Lei

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  1. Yan Liu
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  2. Jianguo Lei
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Correspondence to Jianguo Lei.

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Communicated by L. Teirlinck.

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Liu, Y., Lei, J. More results on large sets of Kirkman triple systems. Des. Codes Cryptogr. 91, 2677–2686 (2023). https://doi.org/10.1007/s10623-023-01221-9

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