[en] We successfully synthesized a dense (∼90%-filled) MgB₂ bulk with no residual Mg via an infiltration process by overcoming the problems in this process such as the expansion of a B precursor disk under a liquid Mg infiltration and the residuals of unreacted Mg in the bulk using a specially designed capsule. As a result, we have achieved a record-high trapped field to date, $B_{\mathrm{T}}$, of 2.4 T at the center of the bulk surface at the lowest temperature of 15.9 K among the infiltration-processed MgB₂ bulks. The trapped-fields simulated for a model with the experimental $J_{\mathrm{c}}({\mathrm{\mu <!--\; ??\; -->}}_{0}H)$ characteristics well reproduced the experimental $B_{\mathrm{T}}$’s and gave a reliable estimated $B_{\mathrm{T}}$ below 15.9 K. The extrapolation of the experimental and simulated $B_{\mathrm{T}}$ curve reached 3 T at 4.2 K. The critical current densities, $J_{\mathrm{c}}({\mathrm{\mu <!--\; ??\; -->}}_{0}H)$’s, at 20 K were 1.8 × 10⁵ A cm⁻² under the self-field and 4.5 × 10³ A cm⁻² under the magnetic-field of ${\mathrm{\mu <!--\; ??\; -->}}_{0}H$ = 3 T. The connectivity, K, of 16% of the present bulk was comparable with that of the ∼50%-filled MgB₂ bulk. The high $B_{\mathrm{T}}$ with low K and the microstructure of the present bulk suggested that the high- and low-$J_{\mathrm{c}}$ regions coexisted because of the wide variation of the MgB₂ grain-size. (paper)