Steiner 3-designs as extensions
Abstract
Abstract In this article, we construct a Steiner system with the parameters S (3, 6, 42), settling one of the smallest open parameter sets of Steiner 3-designs. Furthermore, we establish the existence of rotational Steiner quadruple systems on 46 and 92 points. Our construction method is based on extending Steiner 2-designs using prescribed extension groups. We also consider extensions to designs of higher strength. The article includes a table and a discussion of the status of all admissible parameters for Steiner 3-designs on at most 50 points.
Fields of Study & Subjects
graph theory and CDMA systems
Publication details
- Journal / source
- Designs Codes and Cryptography
- Publisher
- Springer Science and Business Media LLC
- Volume
- 94
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN