(after pre-phasing them together with the UK Biobank samples) and again observed a modest improvement using UK10K imputation (Supplementary Table 14). (We were unable to perform this experiment using HRC imputation because the HRC contains the 1000 Genomes data.) These results demonstrate that high-accuracy pre-phasing is already beneficial for GWAS imputation at current reference sizes (N≈4,000 UK10K samples and N≈32,000 diverse European HRC samples) and that gains will increase as reference panels grow, corroborating our in-sample imputation results projecting high future accuracy with N≈150,000 reference samples.