Let $t>0$ and $\delta\in\big(0,\frac12\big)$ be fixed. For any $k\in\mathbb{N}$ let $I_k,J_k\in\mathbb{N}$ be finite subsets of natural numbers with cardinalities denoted as $|I_k|,|J_k|$, respectively. Now define numbers

$\hspace{70pt}C_k:=\max\Big\{\max\limits_{i\in I_k}i^{2t}\sum\limits_{j\in J_k}j^{2t},\,\,\max\limits_{j\in J_k}j^{2t}\sum\limits_{i\in I_k}i^{2t}\Big\}$

and

$\hspace{70pt}D_k:=\max\Big\{|I_k|\max\limits_{j\in J_k}j^{4t+2\delta},\,\,|J_k|\max\limits_{i\in I_k}i^{4t+2\delta}\Big\}$.

Aim: choose the subsets $|I_k,|J_k|$ so that

$\hspace{100pt}R_k:=\frac{C_k}{D_k}\to\infty\,\,\,\,$as$\,\,\,\,k\to\infty$.