A burner system configured to burn a fuel having a quenching distance, the burner system comprising: - a fuel and oxidant source disposed to output the fuel and the oxidant into a combustion volume to form a fuel and oxidant mixture; and - a perforated reaction holder disposed in the combustion volume, the perforated reaction holder including a perforated reaction holder body defining a plurality of perforations aligned to receive the fuel and oxidant mixture from the fuel and oxidant source; wherein the perforated reaction holder body is bound by a peripheral surface defining a lateral extent of the perforated reaction holder, an input surface disposed to receive the fuel and oxidant mixture, and an output surface facing away from the fuel and oxidant source; wherein the perforations extend from the input surface to the output surface; wherein the perforations each have a lateral dimension D equal to or greater than a quenching distance of the fuel; and wherein the perforated reaction holder is configured to hold a combustion reaction, substantially within the perforated reaction holder, supported by the fuel and oxidant mixture such that a majority of the combustion reaction occurs between an input surface and an output surface of the perforated reaction holder; wherein the fuel and oxidant source comprises: - a fuel nozzle configured to output fuel through a fuel orifice; and - an oxidant source configured to output a fluid including the oxidant; the burner system further comprising: - a perforated reaction holder support structure configured to support the perforated reaction holder at a distance D D from the fuel and oxidant source; wherein the distance D D is 245 times the orifice diameter. - a fuel and oxidant source disposed to output the fuel and the oxidant into a combustion volume to form a fuel and oxidant mixture; and - a perforated reaction holder disposed in the combustion volume, the perforated reaction holder including a perforated reaction holder body defining a plurality of perforations aligned to receive the fuel and oxidant mixture from the fuel and oxidant source; wherein the perforated reaction holder body is bound by a peripheral surface defining a lateral extent of the perforated reaction holder, an input surface disposed to receive the fuel and oxidant mixture, and an output surface facing away from the fuel and oxidant source; wherein the perforations extend from the input surface to the output surface; wherein the perforations each have a lateral dimension D equal to or greater than a quenching distance of the fuel; and wherein the perforated reaction holder is configured to hold a combustion reaction, substantially within the perforated reaction holder, supported by the fuel and oxidant mixture such that a majority of the combustion reaction occurs between an input surface and an output surface of the perforated reaction holder; wherein the fuel and oxidant source comprises: - a fuel nozzle configured to output fuel through a fuel orifice; and - an oxidant source configured to output a fluid including the oxidant; - a perforated reaction holder support structure configured to support the perforated reaction holder at a distance D D from the fuel and oxidant source; wherein the distance D D is 245 times the orifice diameter.