As previously mentioned, "braided" control lines are NOT braided, but twisted. I'm shocked that nobody has provided a link to McMaster-Carr, so I looked it up there. I have not purchased anything from them, but am amazed that they list .015", .016", .018", .020" and .021". Plus various materials, strand configurations and such. I know that our usual stuff is some sort of stainless steel, and McM-Carr lists 18-8, which means that it's 18% Nickle and 8% Chrome. I don't know if the Brodak, SIG and Pylon/Sullivan lines are (or were) the same alloy. I have not bought anything from MBS. Between Brodak, MBS and McMaster-Carr, you've got some options.
https://www.mcmaster.com/products/~/diameter~0-016/?s=.015+stainless+steel+cableAlso, I recall reading that Pylon/Sullivan has been sold and/or moved, but supposed to still be in business. I have ordered direct from them some years ago, and it was a little odd because the shipment actually came from a retail hobby shop, not Sullivan per se. Attempting to support their hobby shop customer by this. What I bought was line clips (Derek Moran style wire ones) and a new switch for the electric finger.
I have some Stellar lines NIP, but don't think I've ever used them. I have used the 19 strand cables Brett mentioned, and he's exactly right on them...too stretchy and too prone to damage. I have also used the "bronzed" cables, and do what I can to AVOID them, because silvery finish shows up much better on grass in the pits. I got a bulk spool of .015 and .018 from RSM, who went out of business some years past.

Steve