Linear combination of unitaries (LCU) block encoding allows for the simulation of a Hermitian operator H on a quantum computer. Specifically, it leverages the representation of a possibly Hermitian matrix as a weighted sum of unitaries in order to embed H into a larger unitary matrix. The exact implementation of this protocol has been discussed in a variety of articles. In this work, we consider a set of possible implementations of an LCU consisting of L terms, detailing the concrete constructions for the required PREP and SELECT operators. The complexity of these is given in terms of T-gate count and we refrain from the use of black box oracle calls. We discuss a protocol allowing for the implementation of SELECT with complexity O(L). The presented PREP operator circuit requires a T-gate count scaling with O(L+log(L/epsilon)), for epsilon the largest absolute error tolerated in the prepared coefficients. We find that by leveraging a tunable number of up to gamma*log(L/epsilon) dirty qubits, the T-gate complexity of PREP may be reduced to O(L/gamma + gamma*log(L/epsilon)). For the optimal value gamma=O(sqrt(L/log(L/epsilon))), this leads to a complexity of O(sqrt(L*log (L/epsilon))).