What is the meaning of sub-constant error?

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The error is defined as $E \geq \frac{1}{2ab(1+ab)}$, where $a$ and $b$ are both positive . The claim is: if we fix the value $a$, then to get a sub-constant error $E$, we must ensure that $b>\frac{1}{a}$. Here, how to understand this claim, i.e. what is the meaning of 'sub-constant'?