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

## TL;DR

This paper extends bounds on the number of resolvable Steiner triple systems of small 3-rank, providing estimates for isomorphism classes of STS of various orders beyond previous exponential bounds.

## Contribution

It generalizes existing bounds on the count of resolvable Steiner triple systems to broader classes of orders with arbitrary factors.

## Key findings

- Derived generalized bounds for the number of isomorphism classes of STS
- Extended previous exponential bounds to more general cases
- Provided estimates for STS of order $v=3^kT$

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