I can offer suggestions which might be considered, but since there are quite a few possibilities, the details would be astronomical.
So, here is something basic and simple:
Typically, the total Line VA for most High Power Factor HIDs in the 400 Watt HPS line would be 480 VA.
At 120VAC, this equates to 4.0 Amps per Luminaire (Ballast + Lamp total package draw).
The commonly used Ballast configuration for the 400 Watt HPS - and the 400 Watt MH too, is the CWA (Constant Wattage Autotransformer).
These Ballasts are able to tolerate +/- 10% Voltage Variations, with about 5% Lamp output variations.
Beyond the 10% input variations, Lamp regulation begins to suffer dramatically, so Voltage Drop is an issue to consider first and foremost.
Many CWA Ballasts are the "Quadri-Volt" types, which have input Voltage taps for:
If the Lighting is to be controlled by multi-pole Lighting Contactors, consider using L-L Voltage for the Fixtures, across different Circuits.
Two - 20 Amp, 2 Pole Circuits from Panelboard.
3 Fixtures on one 2 Pole Circuit,
Remaining 2 Fixtures on the other 2 Pole Circuit.
#10 THHN cu. to first Pole for each 2 Pole Circuit.
If 120VAC is a non-negotiable thing, then break up fixtures across at least 3 Circuits, using no smaller than #10 cu. - unless the fixtures are so close, there will be no Voltage Drop issues.