Parameter space for spherical tokamak reactors is explored quantitatively to elucidate the main constraints for spherical tokamak design choices. Using a constant plasma current Ip search constraint, a set of four Ip scenarios (5, 10, 15, and 20 MA) is first explored in a wide parameter space. Considering modest but gradually increasing auxiliary power, a set of four machine configurations (major radius  = 1.25, 1.75, 2.25, and 3.5 m) is explored next, optimizing the Ip and the bootstrap fraction. Constraints that narrow down the vast parameter space are elaborated along with critical assumptions, such as current drive efficiency, H-mode enhancement factor, nuclear shielding efficiency, and confinement scaling. Limits on the current density of the center post and how it affects the shielding are quantitatively indicated, thereby setting a lower limit on the aspect ratio.