For ground penetrating radar (GPR), smaller antennas would provide considerable practical advantages. Some of which are: portability; ease of use; and higher spatial sampling. A theoretical comparison of the fundamental limits of a small electric field antenna and a small magnetic field antenna shows that the minimum Q constraints are identical. Furthermore, it is shown that only the small magnetic loop antenna can be constructed to approach, arbitrarily closely, the fundamental minimum Q limit. This is achieved with the addition of a high permeability material which reduces energy stored in the magnetic fields. This is of special interest to some GPR applications. For example, applications requiring synthetic aperture data collection would benefit from the increased spatial sampling offered by electrically smaller antennas. Low frequency applications may also benefit, in terms of reduced antenna dimensions, by the use of electrically small antennas. Under these circumstances, a magnetic type antenna should be considered in preference to the typical electric field antenna. Numerical modeling data supports this assertion.