Smallest $(r,r-1)$-erasure correcting set conjecture

For each $r\geq 2$, let $A_{r,r-1}$ be the explicitly constructed $(r,r-1)$-erasure correcting set, and let $F(r,r-1)$ be the minimum cardinality of any such set. Smallest-set conjecture. If $r\geq 2$, then $A_{r,r-1}$ is a smallest possible $(r,r-1)$-erasure correcting set, and

$$F(r,r-1)=2^{r-1}-1.$$

This is presented as an unproved belief after the paper establishes related optimality results, including optimality of the construction for $m=r$.