In my oppinion the current has most influence on the core.
The voltage has most influence on the windings itself .
(arcing at very high voltages , between the wires and between the wire and the core).
Don't forget that Meiyers worked with 26 volts on the primary and a 3 to 1 step up, for 78 volts on the output. 20 KV and 100ma out of a step up is 2000 watts. That is 12 volts and 166 amps on the primary. Needs more than 30 ga wire.
A literal reading of your topic would give recommendations for the alloying ingredients and heat treatment of the core.