1. A system for a server to determine a plurality of lattice points to be referenced to prepare correspondence defining data that defines correspondence between the amount of ink for each color used by a printing apparatus connected to a client and the value of color component in a specific color system, in which: said client has a unit to record the original correspondence defining data which previously prescribes correspondence between the lattice points in the low-dimensional color space prescribed by less color components than the number of inks for each color and the lattice points for ink amount in the ink amount space, a client's communication unit to transmit and receive data through a two-way communication line, and a unit to transmit the original correspondence defining data to the server through the client's communication unit; and said server has a server's communication unit to transmit and receive data through a two-way communication line, a unit to receive the original correspondence defining data through the server's communication unit, a unit to acquire correspondence between lattice points in the low-dimensional color space and lattice points in the device-independent color space by referencing the original correspondence defining data, a unit to prescribe a smoothness evaluation function which evaluates smoothness of the arrangement of lattice points in the device-independent color space and has as a variable the information about the position of lattice points in the low-dimensional color space, a unit to optimize the arrangement of lattice points in the device-independent color-space by improving the rating of the smoothness evaluation function, with the information about the position of lattice points varied, and a unit to determine lattice points for the correspondence defining data by associating the amount of ink for each color corresponding to lattice points in the low-dimensional color space specified by the information about the position of lattice points in the optimized state with lattice points in the low-dimensional color space prescribed by the original correspondence defining data.