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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Communicated by J. D. Key.
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This research is supported by the National Natural Science Foundation of China (61672036), the Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20), the Academic Fund for Outstanding Talents in Universities (gxbjZD03), and the Program of Fundamental Scientific Researches of the Siberian Branch of the Russian Academy of Sciences (0314-2019-0016).
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Shi, M., Xu, L. & Krotov, D.S. On the number of resolvable Steiner triple systems of small 3-rank. Des. Codes Cryptogr. 88, 1037–1046 (2020). https://doi.org/10.1007/s10623-020-00725-y
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DOI: https://doi.org/10.1007/s10623-020-00725-y