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Larger secondary more efficiency?

Hello all,

I need some advice on materials.
(Living in New Zealand, materials are difficult to find.)

My power supply is 15kV -at-120mA, and
I have a large amounts of 24AWG magnet wire 
and 3/16 inch copper refridgeration tubing.  

I would like an 8" or larger secondary, to increase efficiency,
but over 6 inches PVC pipe becomes too expensive for me.
I asked around about cardboard tubes equivalent to sonotube, 
(for forming concrete columns) but all I can obtain 
is 300mm OD tube, (that's 11.8 inches). - BTW this is cheap.

With 120 mA of current, can I use that large a secondary?
(It's all I can get )
I have heard that larger coils are more efficient, but surely
there is a cut off point where efficiency starts to drop as coil forms
get larger?

Thanks in advance,

Alan Williams