Big Images From Digital Cameras

I’m shooting with an 8-megapixel digital SLR. I submitted some images to a lab and requested 24x36-inch prints. I was told that my digital file wasn’t large enough to produce prints of acceptable quality in this size. I’ve had prints made as large as 86 inches from slide film. Do I still need to shoot film for large prints?
T. McGraw
Kansas City, Missouri