The binomial vanishing ideal conjecture for projective sets over finite fields

Let $K=\mathbb{F}_q$ be a finite field, let $\mathbb{Y}$ be a subset of $\mathbb{P}^{s-1}$, and let $I(\mathbb{Y})$ denote its vanishing ideal. A projective set is parameterized by Laurent monomials if it admits a parametrization by Laurent monomials over $K$. Binomial vanishing ideal conjecture. If $I(\mathbb{Y})$ is a binomial ideal, then $\mathbb{Y}$ is a projective set parameterized by Laurent monomials. The conjecture proposes a converse to the preceding result for sets whose points have binary representatives; unlike that restricted case, no such restriction is imposed here, and the supplied source does not indicate whether the conjecture has been resolved.