User blog comment:Deedlit11/Okay, more Turing machines/@comment-10429372-20130927154129/@comment-10429372-20131008172839

Okay, here are some more bounds:

$$\Sigma(21) > f_{\omega+1}(8)$$

$$\Sigma(23) > f_{\omega+1}^2(9)$$

$$\Sigma(24) > f_{\omega+1}^4(2 \uparrow^13 3)$$

$$\Sigma(25) > f_{\omega+1}^12(9)$$