Or you can pick volunteers among the voters to count the ballots as soon as the election closes, right in the polling station. With tables of four volunteers working together and checking each other's work (in addition to the usual party representatives), you get the results within 2 hours and have a really fraud-proof system. It also scales nicely with both the number of polling stations and the population, and needs only 1% to volunteer.
This is how France does it and always has. One of the few places where I won't complain about archaism : it just works, and the 2000 US presidential election fiasco for entire days seemed utterly insane to us.