A Military Pilot on a downwind vector for NTD closely encountered a parachutist about two miles north of CMA.

Narrative

On a mid morning flight we completed our second low approach and were vectored downwind for our third and final prior to returning to base. Our downwind vector was 030/4000'. We got a call of parachute activity 8 miles north of the CMA VORTAC surface to 6000' (maybe 6 miles surface to 8000'). We were passing northwest of the CAM airport by about 2-3NM when we received the call. My situational awareness was that the parachutists were in front of us somewhere; but mentally I pictured them being left of the nose. We had just passed south of some VFR traffic at 4500 and I briefly considered that might have been the jump plane (although it seemed pretty small). We were directed to dirty up (we did) and got the standard stepped turn to final and descent to 2400. I do not recall the exact headings they gave us. Typically they give you a turn to something like 150 then 180 until you get close to final and then turn you the rest of the way. As we were in the turn; we were told parachutes would be in front of us (1 O'clock?) and pretty close (2 miles?) but should be below us. We were given a turn back left across final (back to 140 or something like that). The observer in the rear cockpit saw a canopy go under us on the right side. I did not see it. We were then vectored back to final for an uneventful approach. ATC could have easily extended our downwind a few more miles before turning us to final and we would have completely avoided the area. In fact; ATC turned us pretty much right into the parachute zone. I called NTD ATC and discussed. They stated that they receive minimal warning prior to parachute operations in the vicinity of the final approach.