Method for providing an antenna matrix for transmitting high frequency pulses for influencing a nuclear spin precession in a high-field magnetic resonance tomography system and/or receiving magnetic resonance signals of the nuclear spin precession, wherein the provision takes place in a design process for the antenna matrix, wherein the method has the following steps: Determining a plurality N of different predetermined positions distributed over a predetermined volume; Determining a distribution of a plurality of antenna elements over the predetermined positions; Ascertaining a high frequency pulse or high frequency pulses and gradient pulses for influencing the nuclear spin precession by transmitting the high frequency pulse over the distribution of antenna elements, wherein the high frequency pulse is ascertained by means of solving an optimisation problem under a boundary condition; Reducing the distribution by eliminating an antenna element as a function of the ascertained high frequency pulse; Checking an abort criterion and continuing with the step of ascertaining a high frequency pulse, if the abort criterion is not fulfilled; Providing the antenna matrix with antenna elements according to the distribution of positions distributed over the predetermined volume, characterised in that a local coil is manufactured with a corresponding antenna matrix, wherein the determined not-eliminated positions are populated with antenna elements during manufacture. wherein the method has the following steps: Determining a plurality N of different predetermined positions distributed over a predetermined volume; Determining a distribution of a plurality of antenna elements over the predetermined positions; Ascertaining a high frequency pulse or high frequency pulses and gradient pulses for influencing the nuclear spin precession by transmitting the high frequency pulse over the distribution of antenna elements, wherein the high frequency pulse is ascertained by means of solving an optimisation problem under a boundary condition; Reducing the distribution by eliminating an antenna element as a function of the ascertained high frequency pulse; Checking an abort criterion and continuing with the step of ascertaining a high frequency pulse, if the abort criterion is not fulfilled; Providing the antenna matrix with antenna elements according to the distribution of positions distributed over the predetermined volume, characterised in that a local coil is manufactured with a corresponding antenna matrix, wherein the determined not-eliminated positions are populated with antenna elements during manufacture. Determining a plurality N of different predetermined positions distributed over a predetermined volume; Determining a distribution of a plurality of antenna elements over the predetermined positions; Ascertaining a high frequency pulse or high frequency pulses and gradient pulses for influencing the nuclear spin precession by transmitting the high frequency pulse over the distribution of antenna elements, wherein the high frequency pulse is ascertained by means of solving an optimisation problem under a boundary condition; Reducing the distribution by eliminating an antenna element as a function of the ascertained high frequency pulse; Checking an abort criterion and continuing with the step of ascertaining a high frequency pulse, if the abort criterion is not fulfilled; Providing the antenna matrix with antenna elements according to the distribution of positions distributed over the predetermined volume, characterised in that a local coil is manufactured with a corresponding antenna matrix, wherein the determined not-eliminated positions are populated with antenna elements during manufacture.