Slackened Reed–Solomon list-decoding conjecture

Let $L$ be a positive integer, let $C\geq1$ be a positive real, and let $R=\frac{k}{n}$ be the rate of an $[n,k]$ Reed–Solomon code. A code is list-decodable from radius $\rho$ with list size $L$ if every received word has at most $L$ codewords within relative Hamming distance $\rho$. Slackened Reed–Solomon list-decoding conjecture. For sufficiently large $q$, for most evaluation tuples $(\alpha_1,\ldots,\alpha_n)\in\mathbb{F}_q^n$, the $[n,k]$ Reed–Solomon code evaluated on this tuple is $(\frac{L}{L+1}(1-CR),L)$-list decodable. The conjecture is a relaxation of the capacity prediction by allowing the slack factor $C$; the paper presents it as open and proves only partial parameterized results.