I think the 145/70-6 (DB OEM size) is about the largest 6" tire you're going to find. The Carlisle Straight Rib tire above is 14.44" OD mounted and inflated per Carlisle's spec sheet. That's close to the OD of a typical 145/70-6, the 15x6-6 rib tire is probably a bit wider than a typical 145/70-6. Being a L&G tire, it's engineered for use on grass and dirt at speeds below 10 mph. Carlisle used to have a statement on their website stating that all of their L&G tires were for 10 mph maximum speed. Now it just states that all of their L&G tires are NHS (Non-Highway Service) which basically means they are not to be used on pavement (likely due to rubber compound and construction used). I would not recommend any L&G tire for use on a minibike unless it's only going to be used for putting around the yard below 20 mph.
You didn't state your intended use of the tires. For a large OD tire to be used mainly on pavement, I would suggest this 15x5-6 tire sold by GPS (I haven't seen it elsewhere) but is currently out of stock (like many imported items, due largely to COVID-19).
For an very aggressive off-road tire, I would suggest this SunF tire in size 145/70-6 (DB OEM size).
Those are two extremes in tread design, there are plenty of 145/70-6 chevron (V), lug and knobby tread tires in between. The size, 145/70-6, indicates a section width of 145mm (5.71"), aspect ratio of 70% (sidewall height from bead relative to section width) and the 6 obviously indicates it's for a 6" diameter (at bead) wheel. 145x.
5x2=203 203mm=7.99" 7.99+6=13.99, so call it 14" OD. That's the formula but actual OD and width can vary quite a bit from one tire to another. Again, I doubt you will find much of anything that's larger than the 145/70-6.