@contrex,
Instead of jacking up yer amps, I think your teacher wants you to figure out how you can "get a cheaper lunch". Its really not too difficult. Look at the field equations, it should hit you.
Also, looking at the magnetic permeability portion, have you looked into a nickel iron alloy for the core?. Look up the mag permeabi;lity of Mu- Metal.
We used to use it for old analog (fluxgate) magnetometers