How to get the maximum luminance out of a LED?
I assume you're talking about the basic resistor voltage regulator.  A basic equation for the resistor's value would involve the LED minimum forward voltage (Vf), LED maximum current (If), and power supply maximum voltage (Vs).

R = (Vs - Vf) / If

With supply voltages nearly equal to the LED voltage, it is somewhat hairy as the current may become overly sensitive to the resistor, so I would avoid going below 100 ohms.  A very conservative equation would be as above, but set Vf to zero.

The maximum luminous efficiency of the LED alone would obviously depend on the LED itself, so you would have to look at the datasheet.  For the maximum efficiency of the system as a whole, if driving more than a few LEDs (or any >100 mA LEDs) it would be best to use a switching regulator with current sensing.