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

06/29/2019

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by   Minjia Shi, et al.

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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 STS(v) of rank v-k-1 for an arbitrary v of form 3^kT.