There's an easy way and several difficult ways:
The easy way is to use a set of lookup tables ( the way it used to be done by hand), selecting the table for the number of entries and the number of heats required, (because sometimes selecting 3 out of n heats is fairer than simply 3 out of 3)
The next most difficult way is to use one of the 'static' formulae which determines the order according to a 'fixed' code.
The most difficult way is to have an expert system which selects one of the many grids according to a different set of priorities (eg: number of poles had by each person, changing the grid so that you aren't gridded with the same set all day, good side and bad side of the grid and so on.
I wrote such a system once and it sucked away at the problem for a long time before offering a choice of over 4000 valid answers. It stopped there not because it had finished but because it ran into the 'enough' value.
If you sign up online, then the probability seems to be that the program is one of the static forms which randomises all the entries (so you can no longer gain an advantage by an early or late entry, nor knowing the comp sec) and will produce an answer with an acceptable number of violations. (Except for certain grids it is impossible to give every the same number of 'grid start' points, the trick is to minimise the number who differ from the norm).
With this method, solutions such as number of poles etc is controlled by derandomising the initial grid, rather than meeting an exact set of conditions for each grid.
Drivers seem to be mixed, some prefer to grid with different people each grid in the day, others prefer that they should keep the same people around them for each grid of the day.
And it seems that the service is offered by Alpha Timing along with the online entry forms and race results output.
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