In our office, we have split our spaces into equal amounts of users. The group work it out amongst themselves, but most groups go for a full week of having a space.
So in your instance, you have 25 spaces/100 drivers (excluding the management), so that's four drivers per space. Ascertain whether any P/T workers have "opposite" days, for instance Julie works Mon/Tues, and Jamie works Weds/Thurs/Fri. They would be considered as one driver, as would a couple. No dodgy double deals allowed!
Then it's up to the four drivers to decide what works best for them... if they are off, they can swap weeks, and even odd days, and only have to be in touch with the three other drivers in their group.
Establish if all 100 people actually want to be classed as drivers though... in our office a guy wanted to make sure he was entitled to a space just in case he may need it sometime in the future...., even though he didn't have a car, and hadn't driven for over 20 years! Some people eh?
All I can say is that this system does work, and is super easy to administer as it is basically the team's responsibility to organise themselves.
Good luck! This was a massive problem when we moved from unlimited spaces to a new office with a tiny carpark!