Learjet 45 flight crew reported a rejected takeoff and runway excursion after the Number 1 and 2 tires ruptured and departed the wheels.

Narrative

During the takeoff roll using Runway XX at ZZZ the number one and number two tires ruptured and departed the wheels. This occurred within 10-15 kts of attaining V1 speed (105 kts for this takeoff). The pilots first heard two muffled explosions less than one second apart and immediately felt the aircraft lean slightly to the left and felt and heard the bumping of bare wheels on pavement. The abort call was verbalized by the Pilot Monitoring (PM) (the PIC) the Pilot Flying (PF) immediately aborted the takeoff. The PF decelerated the aircraft on the centerline until at or below an estimated 40 kts. At or below approximately 40 kts; the airplane began a smooth departure from the centerline moving toward the right side of the runway. As movement to the right progressed; the PM reduced reverse thrust on the right engine and held full reverse thrust on the left engine. The aircraft stopped with the nosewheel an estimated 10 feet from the right edge of Runway XX and at 4;700-4;750 feet down Runway XX. The aircraft started the takeoff roll with the main gear at an estimated 35-50 feet from the Runway XX end-line. Following are a collection of observations:1. One tire was found mostly intact but with a ruptured sidewall. It was located approximately 50 feet to the left of the runway pavement at approximately 2;000 feet down the runway.2. Grooving of the runway surface made by the bare wheels was observed for approximately the last 2;400 feet of aircraft travel.3. A ring of metal that seemed to be part of the wheel assembly was found at 1;300 feet down the runway and in the middle of the runway.4. After the aircraft was stopped; the PIC exited the aircraft to inspect for hazards and noted a trail of light smoke coming from the left brakes; probably because hydraulic fluid was leaking from a hydraulic line near the hot brakes. Other than obvious damage; no additional hazards were noted.