Start with LilGun powder and a small pistol primer. At some point, try a small rifle primer as well. Some loads just prefer one primer over the other.
Hodgdon Powder says that LilGun can give up to 200fps more speed and lower the pressures by 10k-psi.
Change the powder level by .2gr (2/10ths) until you find accuracy. On several different Hornets, I found best accuracy at the top of the powder charge. Depending on what brass you use, 13.0 is about all I can get into the case.
On such a small case as the Hornet, little changes, such as .1gr in powder, can make big changes at the range.
I use a Lee Collet Die to neck size my brass.
Another powder that shows promise in the Hornet is Alliant 300-MP, giving similar velocities to LilGun, but Alliant does not publish the pressure data. I have not used 300-MP.
