Asymptotic conjecture that the normalized constants $\alpha_r$ vanish

For fixed $r\geq 1$, let $\alpha_r$ be the smallest real number such that

$$f_r(n)\leq \alpha_r(1+o(1))\binom{n}{\lfloor r/2\rfloor}.$$

Here $f_r(n)$ is the minimum number of complete $r$-partite $r$-graphs needed to decompose the complete $r$-graph on $n$ vertices.

Vanishing-$\alpha_r$ conjecture. We have

$$\alpha_r\rightarrow 0\quad\text{as }r\rightarrow\infty.$$

The initial construction gives $\alpha_r\leq 1$ for all $r$, while the paper establishes $\alpha_r\leq \frac{14}{15}$ for even $r$. The conjecture predicts a substantially stronger improvement as the uniformity grows.