Tradeoff between repair bandwidth and sub-packetization for Reed–Solomon codes

Let $[n,k]$ denote a Reed–Solomon code with an $\epsilon$-MSR repair scheme, meaning that the repair bandwidth for every single failed node is at most $(1+\epsilon)$ times the cut-set bound. The tradeoff conjecture. Any $[n,k]$ $\epsilon$-MSR Reed–Solomon code has sub-packetization $(n-k)^{\Omega(1/\epsilon)}$, and this is tight up to a constant factor in the exponent. The paper's constructions achieve polynomial sub-packetization in the constant-rate regime, including $(n-k)^{O(1/\epsilon)}$ for its $\epsilon$-MSR family; the conjecture asserts that this dependence on $\epsilon$ is essentially optimal.