So, if one wants a 16 ga secondary, look at wire with half this x-section area. 19 ga. Put two of them side by side in parallel. Bi-filar is the term for this method. This method also doubles the pitch of the wind, and cuts the number of turns per axial inch in half.
Reducing the pitch is a good thing for high ratio designs. 10k:8R requires a turns ratio of ~35:1. We can get the whole layer covered, without resorting to leaving space between the wires.

Winding bi-filar is a PiTA. I have tried it with 26 ga. Took making a few kilos of copper wire scrap before I had anything which looked reasonable. NC machines are soooooo much better at this sort of thing. Faster too.
cheers,
Douglas