Plumbing Question: Venting the drains on a bathroom basement?

I am putting in a bathroom in my basement. No previous plumbing! My issue is venting the toilet. I am putting the toilet on the opposite side of where i need to connect to the venting. Going straight up and over is not an option. There are doors on both sides of the toilet, and going over the doors, following the wall around to the venting also is not an option. I've looked at loop venting but can't find very much information on it. Any thoughts? If I did loop venting it would have to go up and over the door, down on the other side, than follow the wall around and connect to the venting. The toilet is right next to the 28inch door.

(Side question: does venting need an incline or not? I've heard it does, and that it doesn't - Thanks again)
Thank you for any thoughts!!!

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