RRP codes exceed the LMRD bound outside the exceptional packet lengths

Let $v$ be a packet length, and let the RRP denote the construction problem referred to in the source. The LMRD code bound is the benchmark bound for lifted maximum-rank-distance codes; the echelon-Ferrers construction and its variants are competing constructions.

RRP bound conjecture. For any packet length $v\geq 7$ with $v\notin\{8,10\}$, the largest subspace codes that can be obtained by solving the RRP exceed the LMRD code bound and thus are better than the codes resulting from the echelon-Ferrers construction and its variants.

The claim is motivated by computational results for packet lengths through $15$, but the supplied text does not establish it for every stated $v$ and gives no resolution beyond those computations.