secondary core other than air

["Garth van Sittert" <garth-at-mediasupplies.co.za> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

Would it be possible to use something other than an air core to increase the
secondary inductance and Q factor?
 
Are their any possible cores available?  I know something like ferrite core
would create internal arcs, but surely there must be something out there!
 
I have just wound my 6.4" secondary with what I was told to be #24 wire,  but
wintesla seems to use incorrect figures for wire guage and turns per inch.  My
secondary has 33 turns/inch.  
 
My secondary inductance is way too low and I now have re-calculated my primary
with only 5 turns which I think will be terrible for spark gap losses.  My
topload is 20" wide so I can't drop secondary resonance any more unless I use
some secondary core other than air or wind more turns on the secondary.