3 problems

Steiner triple code embedding-dimension conjecture. For every $d\ge 1$ there exists a Steiner triple code $\mathcal{C}$ with

Effective-bound conjecture. These three quantities equal $2^k-1$ for $k\geq 1$. This conjecture gives the expected sharp value of the embedding dimension bound for the incidence st…

Let $S$ be a good subsemigroup of $\mathbb{N}^2$. Its multiplicity vector is denoted by $\boldsymbol{e}$, and let $M=S\setminus\{\boldsymbol{0}\}$. A good semigroup is said to have…