Number of polyominoes with area $n$

Question

On paper A procedure for improving the upper bound for the number of $n$-ominoes by D. A. Klarner & R. L. Rivest, it is known that the number $t(n)$ of polyominoes with area $n$ satisfies $3.72^n<t(n)<6.75^n$. What is the best current result?

Answer 1

Wikipedia suggests that no-one has improved on Klarner, D.A.; Rivest, R.L. (1973) A procedure for improving the upper bound for the number of n-ominoes, Canadian J of Math. 25 (3): 585–602, which gives $$\lim_{n \to \infty} (t(n))^{1/n} \le 4.649551$$

However, that is not conclusive because it appears to overlook Barequet, G., Rote, G., & Shalah, M. (2016) λ> 4: An improved lower bound on the growth constant of polyominoes, CACM, 59(7), 88-95, which gives a lower bound of $$t(n) \ge 4.00253176^n$$

Two of the same authors (Gill Barequet, Mira Shalah) have a preprint on arxiv which purports to show that the upper bound is $$t(n) \le 4.5252^n$$