Average puncture bound for covering with Reed–Solomon codes

Let $C$ be an $[n,k,d]_q$ generalized Reed–Solomon (GRS) code, and consider the covering algorithm that repeatedly punctures the received word and applies a GRS decoder. Let $c_1,c_2$ be positive constants with $c_1,c_2<1$. Average puncture conjecture. The average number of punctures needed for the algorithm to return a codeword within the covering radius is less than $c_1(d-1)$ when the GRS decoder is a unique decoder, and less than $c_2$ when it is the Guruswami–Sudan list decoder. This conjecture concerns the average-case complexity of the covering algorithm; the supplied text gives empirical data as motivation but does not state a resolution, so the claim remains open.