Air carrier Captain reported receiving a low altitude alert from ATC on approach to LAX; citing possible miscommunication with ATC as contributing.

Narrative

While on descent for turn to final approach; autopilot engaged; we were given a descent clearance to 1;600 feet. This is a low altitude; but we were being vectored for our base turn shortly. We were told to; 'Expedite descent.' We all know ATC has minimum vectoring altitudes that aren't listed in our charts. When the clearance was given; my pilot monitoring FO set the altitude and pointed at the number without speaking it as is company policy. I confirmed that was the altitude given by pointing at the number and stating '1;600 feet.'Our relief FO was also in the flight deck during this final phase and had been for several hours. We all three heard the clearance. As we descended through 2;000 feet ATC said; 'Low altitude alert. Climb immediately to 2;600.' My monitoring FO read back the clearance and put in the new altitude and pointed; I pointed and stated 2;600 feet while engaging Flight Level Change. The plane smoothly climbed 600 feet. At this point I stated that I had initially heard 1;600. My monitoring FO said that's what she heard too. The relief FO said that the controller DID say 1;600 feet. I'm confident that all three of us heard what we were assigned. At the time we clearly had the ground in site and visibility was such that when we were turned towards the airport that we had the runway in sight. Instrument and visual approaches were being conducted. The rest of the flight was uneventful.