Often I find myself needing to know the best error correcting code for a certain quantum scenario. For example, suppose my logical systems are 3-dimensional; then what's the most efficient encoding to resist at most 4 single-system errors? Of, suppose my logical systems are qubits; then what's the most efficient encoding to resist 5 single-qubit phase errors?
Presumably for many questions like this, the answers are known. Is there a good survey that gives the state-of-the-art?