Existence of [8,3]_{q^6/q} rank-metric intersecting codes

Determine whether, for any prime power q, there exists a nondegenerate [8,3,d]_{q^6/q} rank-metric intersecting code for some minimum distance d.

Background

Within the detailed discussion of the m=6 case, the authors enumerate known existence results for [n,3]_{q^6/q} rank-metric intersecting codes, covering n=5–7 and n=9, and establish non-existence for n<5 and n>9. The intermediate case n=8 is singled out as unresolved.

They further note that attempts to obtain such a code via rank-metric puncturing from known constructions were unsuccessful, underscoring the difficulty of this specific instance.