Improving upper and lower bounds of the number of games born by day 4

In combinatorial game theory, the lower and upper bounds of the number of games born by day $4$ have been recognized as $3.0\cdot {10}^{12}$ and ${10}^{434}$, respectively. In this study, we improve the lower bound to ${10}^{28.2}$ and the upper bound to $4.0\cdot {10}^{184}$, respectively.