A high supersonic, shocked and heated jet at a Reynolds number of 105 is computed by large-eddy simulations (LES) to directly determine its radiated sound field, using low-dissipation schemes in combination with an adaptative shock-capturing method. The jet exit parameters are a Mach number of Me = ue/ce = 3.30, a static pressure of Pe = 0.5 × 105 Pa and a static temperature of Te = 360 K, where ue and ce are the exit velocity and sound speed. The aerodynamic and the near acoustic fields are compared with to theoretical results and experimental data. Some insights into the far acoustic field are finally shown.