Impact of ordering Hamiltonian terms for Trotterization

In Trotterization, the typical Hamiltonian considered is:

$$ H = sum_{p, q} h_{pq} a^{dagger}_p a_q + sum_{p, q, r, s} a^{dagger}_p a^{dagger}_q a_r a_s $$

Which is then converted into a sequence of gates by the Jordan Wigner transformation.

However, how do we choose the ordering of the $ pq$ and $pqrs$ terms? For example, if our Hamiltonian was:

$$ H = (a^{dagger}_1 a_2 + a^{dagger}_2 a_1) + (a^{dagger}_2 a_3 + a^{dagger}_3 a_2) + (a^{dagger}_1 a^{dagger}_2 a_2 a_3 + a^{dagger}_3 a^{dagger}_2 a_2 a_1)$$

There are at least $ 3! = 6$ ways to order the Hamiltonian, a number which quickly explodes as the size of the Hamiltonian grows.

Note that the terms don’t have clean commutation rules – sometimes the terms will commute or anticommute. Is there an approach to ordering the Hamiltonian that maximizes simulation accuracy?