AN ACR DISPATCHER FINDS HE CANNOT COMMUNICATE WITH FLTS IN MEXICAN AIRSPACE AS REQUIRED BY FAR.

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CAPT XXX CONTACTED ME WANTING TO KNOW HOW I WOULD BE ABLE TO CONTACT HIM ONCE HE WAS IN MEXICAN AIRSPACE (MKE-PVR). I INFORMED HIM THAT CONTACT COULD BE MAINTAINED VIA COMMERCIAL RADIO THROUGH HRL OR THROUGH COM FOR APPROX 150 MI FROM THE HRL XMITTER. AFTER THAT; WE SHOULD BE ABLE TO CONTACT THEM THROUGH ATL RADIO ON FREQ 130.1. I ADVISED HIM THAT TECHNICAL SUPPORT ADVISED ME THAT WE SHOULD BE ABLE TO CONTACT THEM ON THAT FREQ FOR OVER 200 MI RADIUS OF THE TAM/MEX/GDL VORS OR RADIO XMITTERS/RECEIVERS. THE CURRENT OR FLT PLANNED ROUTING WOULD KEEP THEM WITHIN RANGE. I TOLD HIM THAT I WOULD ATTEMPT TO CONTACT THEM IN 30 MINS WHICH WOULD BE APPROX XA20Z. I TRIED OR ATTEMPTED TO THEN; AND 2 OTHER TIMES; AND WAS NOT ABLE TO CONTACT THEM. I DISCUSSED THE RANGE OF THESE MEXICAN XMITTERS WITH THE ATL RADIO SUPVR AND SHE TOLD ME 100 MI WOULD BE GUARANTEED; 150 MI WAS A STRETCH; AND 200 MI WAS THE FARTHEST BUT THAT WAS ONLY IN THE CARIBBEAN. THIS HAPPENED ON JAN/SAT/02. I HAVE HAD NO FORMAL TRAINING AT ALL ON THIS OP WITH THE B737-800.