Interstellar TV: Calculating Detection Range

[Urvabara]

I am just "trying" to watch interstellar TV...

The detection range in lightyears is
$$R = \sqrt{\frac{\text{EIRP}\cdot A_{e}_{r}\cdot\text{twc}}{4\pi\cdot\text{SNR}\cdot B_{r}\cdot k_{B}\cdot T_{sys}}}\cdot\frac{1\,\text{ly}}{9454254955488000\,\text{m}}$$, where
$$\text{EIRP} = P_{t}G_{t},$$
$$\text{twc} = \sqrt{B_{r}t} = 1\,\text{for modulated signals,}$$
$$\text{SNR}$$ is signal-to-noise ratio,
$$A_{e}_{r}$$ is receiver's radio telescope's effective area,
$$B_{r}$$ is receiver's bandwidth which is larger or equal to transmitters bandwidth,
$$k_{B}$$ is Boltzmann's constant and
$$T_{sys}$$ is system's temperature in Kelvins.

I put these numbers in:
$$\text{EIRP} = 15000\,\text{W}$$,
$$A_{e}_{r} = 15707963\,\text{m}^{2}$$,
$$\text{twc} = 1$$,
$$\text{SNR} = 22$$,
$$B_{r} = 8\cdot 10^{6}\,\text{Hz}$$,
$$k_{b} = 1.3806504\cdot 10^{-23}\,\text{J/K}$$, and
$$T_{sys} = 10\,\text{K}$$.
I get: $$R = 0.000093\,\text{ly}.$$

Questions:
1. Is the equation correct?
2. Is my answer about correct?
3. How to reduce the SNR?
4. How to reduce the system temperature?
5. Can I really rise the detection range just only reducing the system temperature? So technically I can watch interstellar TV shows with a very, very small disc, if I can go to very near the absolute zero?

 

[Urvabara]

Guys? Anyone?

PS.
$$P_{t}$$ is transmitter's power.
$$G_{t}$$ is transmitter's antenna gain.