Entrance cable size for a 800’ distance to feed a 100 amp breaker box
Throwing aluminum at the problem is bad for your wallet
The problem with runs of this length is that simply throwing aluminum at your problem adds up fast (don't even bother with copper for this).  In particular, you're looking at parallel sets of 250 or 350kcmil Al if you are bent on making this run at 240V within your voltage drop criteria; even doing it as cheaply as possible by using paired URD triplex with a single 3/0 neutral + 3/0 EGC in 3&quot; PVC, you're still looking at upwards of $6k, and that's fudging things a bit with the 250kcmil Al to get a voltage drop of 3.3%.
Interpreting your criteria strictly, with paralleled 350kcmil pairs for the hot legs and a single 4/0 neutral with the other 4/0 used as the EGC, puts us well over $7k at the time of this writing, and it only gets worse from there if you need to control voltage drop on the neutral over this length.  From this, we can conclude that something has to give, whether it be your voltage drop criterion, your wallet, or something else.
Transformers to the rescue!
The good news is there is something else that can give, and that is the voltage you make this run at.  Nothing in the NEC prohibits you from wielding the reason Tesla won the war of the currents to your advantage by installing a pair of distribution transformers, one at the main disconnect and the other at your load.  While the transformer pair alone will set you back $2k + another ~$200 in shipping and handling (which is understandable, given that a 25kVA single phase transformer tips the scales at almost 300lbs by itself), the savings on wire you get makes the investment more than worthwhile.
In particular, with a 100A load, 3% drop on the wires, and an 800' run, it's possible to step the voltage up to 480V with the aforementioned transformers for the run, allowing you to use a single 2/0 triplex cable in 2&quot; PVC conduit.  This puts you out a mere $2k for the wires and conduit in the long run; you'll need appropriate wiring methods for main-panel-to-transformer and transformer-to-load, as well as a 60A, 600V rated, Class RK5 time-delay fuse and matching fuseblock to protect the long run itself, but none of those are a major setback cost-wise. (You could use liquidtight flexible conduit or type SE cable for the the 240V runs, and the fuse and fuseblock mentioned will set you back about $50 while living quietly at the bottom of the meter-box transformer's wiring compartment.)
Transformer wiring notes
First off, if you're not comfortable wiring up 480V yourself, there is nothing wrong with calling in an electrician for this work; anybody well-versed in commercial or industrial work should be able to handle wiring this up without an issue.  Nonetheless, if you want to know more about how this is wired once the conductors are in the ground, read on.
We start at the meter-box transformer, where the 240V hots connect to X1 and X4, while X2 and X3 are jumpered together, and the grounding wire from the meter-main connects to a case grounding lug on the transformer.  The fuse block then gets bolted into the bottom of the transformer's wiring compartment; once this is done, H2 and H3 are jumpered together, and H1 is jumpered to one fuseblock terminal.  The outgoing wires (taped brown/grey to avoid confusion with 240V wiring!) are then landed on the open fuseblock terminal and H4, while the striped wire in the outgoing triplex lands on the transformer's other grounding lug.  Finally, a stacked lug on H4 is used to connect the system bonding jumper to a third grounding lug on the transformer case, thus grounding the transformer's secondary side via the combination EGC/GEC running up to the meter-disconnect and its ground rods.
We then move onto the load-end transformer.  Here, H2 is jumpered to H3 again, with the incoming wires landing on H1 and H4, and the striped wire landing on a transformer grounding lug, of course.  However, we wire the secondary for 120/240V split-phase, with X1 and X4 connecting to the outgoing hot legs, and X2 and X3 connecting to each other, the outgoing neutral wire, and a system bonding jumper to the other transformer grounding lug.  (This seemingly redundant bonding jumper is permitted by Exception 2 to NEC 250.30(A)(1) provided you don't have any other metal paths between the transformer and the load's distribution panel.)
Finally, we land the incoming secondary wires from the load-end transformer on the main terminals of the load's distribution panel.  Given the situation you're in, you'll want to use a 100A main breaker panel (you can get larger busses, but you need the main to be 100A in this case) for this job.  Note that you'll need to make sure this panel has its bonding strap or screw fitted, as well, as we're bringing hot/hot/neutral up from the transformer to the panel in this case.
If you'd rather bring 4 wires up from the transformer to your load, though, that is possible, but requires you to decide whether your system bonding jumper for your load lives in the transformer enclosure or in the distribution panel.  You can even have the transformer live inside instead of outside as I have been presuming in the above discussion, but that requires you to use a 4-wire connection between said transformer and the load's distribution panel.