  We analyze the resource overhead of recently proposed methods for universal
fault-tolerant quantum computation using concatenated codes. Namely, we examine
the concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller
code, which allows for the construction of the 49 and 105-qubit codes that do
not require the need for magic state distillation for universality. We compute
a lower bound for the adversarial noise threshold of the 105-qubit code and
find it to be $8.33\times 10^{-6}.$ We obtain a depolarizing noise threshold
for the 49-qubit code of $9.69\times 10^{-4}$ which is competitive with the
105-qubit threshold result of $1.28\times 10^{-3}$. We then provide lower
bounds on the resource requirements of the 49 and 105-qubit codes and compare
them with the surface code implementation of a logical $T$ gate using magic
state distillation. For the sampled input error rates and noise model, we find
that the surface code achieves a smaller overhead compared to our concatenated
schemes.
