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The phrase "achieve the lower" is not correct and does not convey a clear meaning in written English.
It may be intended to express reaching a lower level or standard, but it lacks context to be usable.
Example: "Our goal is to achieve the lower cost of production without sacrificing quality."
Alternatives: "reach the lower" or "attain the lower".
Exact(28)
The asymptotics of the resulting code lengths further show that these schemes are capacity-achieving; asymptotically, the code lengths achieve the lower bounds that follow from the simple capacities, as derived in [26].
Mr. Carty called the proposed cuts "an enormous challenge," but said he was confident the airline could achieve the lower spending levels.
We will prove that the ACO-OFDM can achieve the lower bound.
It is shown that only one iteration is needed to achieve the lower bound at high SNRs.
Secondly, to reduce the implementation complexity, we achieve the lower bounds of outage probability and average SER.
The user who is able to decode the base bits of the hierarchical constellation can achieve the lower resolution.
Similar(32)
The administration expects to achieve the lowered hospital payments in two major ways, by slowing the growth of reimbursements.
Rather than indiscriminately handing out more tax incentives, Mr. Gore and Mr. Bush should consider simplifying the code and achieving the lower tax rates they think the voters are demanding in an across-the-board but progressive way.
Self-portrait With a Palette, painted by Manet in 1878, had been estimated at between £20 and £30m, and the fact that it achieved the lower end of the estimate could even be seen as a disappointment, given some of the extraordinary prices paid for top-end art this year.
Table 1 denotes that our scheme significantly achieves the lower packet loss ratio compared to SPF, CODA, ESRT, and GRATA.
A U-type design is E fNOD -optimal if its E fNOD -optimalchifves the lower bound.
More suggestions(1)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com