(This is basically a reference request)
I am wondering if there are any results out there on to what accuracy a given unitary can be approximated with an element drawn from a t-design.
To elaborate a bit, consider the Haar measure over $U(d)$. This integrates over all the unitaries in $U(d)$. So we could say that given some fixed unitary $U_0$, there is an element in the set of unitaries integrated over by the Haar measure which approximates $U_0$ well (this is trivial of course, since $U_0$ itself occurs in the integration).
Now consider a $t$-design. The $t$-design is a finite set of unitaries which has some special properties - namely summing over that set approximates doing a Haar integral. Heuristically, the set of unitaries in the $t$-design looks like the full set of unitaries. So now given some specific unitary $U_0\in U(d)$, is it the case that some element of the $t$-design must be close to $U_0$?