Basement Toilet venting requirements

Hi - I hate to beat a dead horse, lots of questions about venting that have been answered, but I'm not seeing any that deal with tying into a horizontal waste stack from the basement. I am plumbing in a new bath - see diagram attached:

I only have about 16" from the toilet sweep to where it attaches to the main waste line (running horizontal). That allows me to use a long sweep 3 x 3 x 3 long sweep wye, but no additional 3 x 3 x 2" vent t to vent the toilet separately.

I am running 1 1/2" drain from sink thorugh the wet wall to the right of the toilet (see diagram). This has a 2 x 2 x 1 1/2 waste t where I drain down and connect to the 2" shower drain. This line then connects into the horizontal drain with a separate 3 x 3 x 2 long sweep. I am running a 2" separate vent that will exit through the roof of my 3 story house so this set of fixtures in the basement has it's own venting system.

I believe my shower and sink are properly vented, but I'm wondering if I have to have a separate vent for the toilet since it is 16" from the main stack (that is vented out the roof as well but is the main waste stack for the bathrooms upstairs as well).

Also, is there any code that specifies the distance between branch lines coming into the 3" waste line. Currently my plan is that the 3 x 3 x 3 wye for the toilet and the 3 x 3 x 2 wye for the shower/sink drain puts them about 12" apart.

Finally (sorry to be so long winded) - if I do have to have a separate vent from the toilet that ties into my 2" vent, any recommendations on how to get all this into the 16" space... I could not find a 3x3x2 with closet end to do it...if it exists, I would be perfect, I am only 1" off with the vent t included.
Thanks for the help.

P.S. - My main branch is 10" deep so I have enough room for my slopes on all my lines with the 45degree vents off the lines & 3" of concrete.

"I only have about 16" from the toilet sweep to where it attaches to the main waste line (running horizontal). That allows me to use a long sweep 3 x 3 x 3 long sweep wye, but no additional 3 x 3 x 2" vent t to vent the toilet separately."

bigred,
You don't get out of it that easy. The toilet must be vented. If you have to take out more concrete, then you will.
If you need more room, you can put the wye and a 45 farther downstream.
This way you can throw in a rolled 3"x2" wye for the vent remembering to use waste fittings below the flood level of the fixtures.
I would not wet vent the lav into the shower.
Run them seperately, the vent for the shower can revent into the lav vent at 42".
If you decide the wet vent the lav with the shower, keep the vented portion either vertical or at a 45%. You could run the 2" line under the plumbing wall to achieve that and then "arm" over to the center of the shower pan.

One way to to do this would be to wye off sooner and run a line under the plumbing wall for everything. The toilet would wye off again from that line with a rolled wye fitting for the vent. The lav and shower would run under the wall too until the shower was wyed off and vented. If the lav was wet vented over the shower, then it would run straight from there until the lav was pulled off and then you could arm over for the shower trap.

Deb

As Terry has mentioned, this will not work. I would recommend you call a plumber for some layout help. When you have close clearances like this,It can get complicated.
The toilet MUST be vented. Do not go on with your plan like it is. Wives get real cranky about toilets that do not work.
Deb
The Pipewench