Optimal ordering conjecture for divided decoding split sizes

Let $\hat{\mathbf{s}}$, $\hat{\mathbf{s}}_M$, or $\hat{\mathbf{s}}_{\epsilon}$ be approximated by divided decoding with sphere decoding according to a splitting index set $\{i_0,i_1,\dots,i_k\}$ satisfying

$$1\leq i_0<i_1<\cdots<i_k<n,$$

whose fixed sub-vector size set is $\{n_f\}_{f=1}^{k+2}$, where $n_f=i_{f-1}-i_{f-2}$. Optimal ordering conjecture. Among index sets with this fixed sub-vector size set, the index set for which

$$n_1\leq n_2\leq\cdots\leq n_{k+2}$$

is the best choice: it simultaneously minimizes the error rate and the decoding complexity. The claim proposes a joint optimum for error performance and complexity when the split sizes are arranged in nondecreasing order; the surrounding discussion motivates it by comparing split orders with identical sub-vector sizes but different error rates and diversity orders. No proof or resolution is supplied in the source.