An improved lower bound for the blowup defective chromatic separation constant

For a graph $G$ and an integer $d \geq 0$, let $χ^d(G)$ denote the $d$-defective chromatic number, and let $G \boxtimes K_{d+1}$ be the $(d+1)$-fold clique blowup of $G$. Norin and Steiner disproved the conjecture $χ(G) = χ^d(G \boxtimes K_{d+1})$ of Guo, Kang and Zwaneveld by exhibiting, for infini