smallest tyres for 45mm rims?

I have some 27.5 x 45 rims and 3inch tyres on the bike I use for DH trails but feel the bike slipping out on burns because they don't dig in.
How thin a tyre can go on 45mm rims without pushing my luck?
How thin a tyre can go on 45mm rims without pushing my luck?
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Think it would be worth thinner rims or can I get away with thinner tyres on 45mm rims
https://www.schwalbe.com/en-GB/reifenmasse.html
When the link opens, click on "which tyre fits which rim?" and then page down to the chart.
It looks like 70mm (2.76") is the smallest for a 45mm rim.