An important advantage of a coplanar transmitting array is that it can be both thin and flat, while the radius of the transmitting coils can be large to provide the required strength of magnetic fields. To take full advantage of the flat transmitter, we find in this work the minimum number of transmitting coils that is required for unambiguous tracking and also their optimal patterns that provide the best possible tracking precision over a given operating volume. To solve this task, we use the differential evolution algorithm. A new scleral search coil (SSC) tracking approach employing a planar transmitter has been developed and tested experimentally. Such transmitter is much more convenient in installation, operation, and maintenance than the conventional large cubic one. It also increases the mobility of SSC systems, simplifies their accommodation in a limited clinical space, enables bedside testing, and causes no visual distractions and no discomfort to the patients. Moreover, it allows tracking not only the SSC orientation, but also its location. The suggested approach provides the speed and precision that are required in SSC applications.