Why forty shots cannot pass this Hoeffding certificate

This is a limitation of a specified sufficient procedure, not a universal lower bound on all recovery experiments or all confidence methods. It gives a local proof of the limitation reported for Oai280-A/B CheungOai280AB.

For one task with equal shot counts $n$ and allocations ${\delta }_i={\alpha }_{\mathrm{s}}/3$, the best possible correlations give

Thus passing even in that ideal-data case requires