As IRstuff pointed out, and antenna would need to be 78 inches in diameter. But an antenna uses air with a dielectric constant of 1. If you use what is called a dielectric lense the size will be smaller. This substitutes a substance with a higher dielectric constant which makes the antenna smaller. I have seen specialized antennas using a dielectric antenna made of teflon
But, this is the extent of my knowledge in this area.