what size joist under oak flooring?

[somewhereinthehills]

Hi, i'm soon to be laying a new oak strip floor in our barn conversion.
the existing joists are 200mm2 oak, with a 150x38 softwood joist bolted to each side. The oak is centered at around 700-800mm. The oak flooring is 75x25mm random length.
I know that i need to put in some extra support, as the current gap is way to large for a suitable installation, but what i don't know is what size joist to use. The oak flexes very little when you stand on it, so i'm thinking extra joists of 150x38 is total overkill. i was thinking something in the region of 100x38, or maybe 75x50?
many thanks for any suggestions.

 

[WoodYouLike]

The oak flooring is 75x25mm random length.

Installing a wood floor directly onto joist can be safely done if:

the joist are not further apart than 35 - 40cm
every board connects at least with 3 joists
extra joists should at least have a 75mm surface and at least 50cm thick