I suspect you are right that HLL+TC will be more accurate. Based on Figure 5 vs. Figure 1 in the Ertl paper, I think Ert's method improves HLL estimation for lo

I suspect you are right that HLL+TC will be more accurate. Based on Figure 5 vs. Figure 1 in the Ertl paper, I think Ert's method improves HLL estimation for low cardialities and for very high cardinalities, but not for the region where HLL is already at its most accurate.