What question did this study set out to answer?

To explore new constructions of Steiner Triple Systems (STS) of specific types and order.

March 5, 2026Open Access

Some Constructions of Steiner Triple Systems of Type v⟶2v + 1 + 6k

LFL. FragapaneUniversity of Catania MGMario GionfriddoUniversity of Catania

Key Points

To explore new constructions of Steiner Triple Systems (STS) of specific types and order.
Analyzed the properties of Steiner Triple Systems of order v.
Investigated constructions of STS(v) for types v≥v+20 and v≥v+40.
Examined all possible cases of formations within the defined parameters.
Identified unique structures within the larger category of Steiner Triple Systems.
Demonstrated that both STS types can be constructed under the given conditions.

Abstract

A Steiner Triple System (STS) of order v is a hypergraph Σ=(X,B) that is uniform of rank 3 and has order v, such that every 2-subset of X has degree 1. In this paper, we present some constructions of STS(v) of type v⟶v+20 and v⟶v+40, examining all possible cases.

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