I'm a programmer, not a mathematician, but knowing that the probability of any payout match on a single grid is given by
$p = _pC_r / _nC_r$, where $r$ is the number of matches required for a payout and
$(r <= q)$,
intuitively, having $1/p$ grids covering all r-tuples will result in a probability of $1$ - a guarantee.
However (unfortunately) I don't believe there exists a design for a $1/p$ set of grids covering all r-tuples uniquely (my brute force computer trials have all failed), but I don't have the math skills to prove it. Such sets exist, but with many more than $1/p$ members.
As a side note, this concept was implemented successfully by a group who purchased several hundred grids weekly with a guaranteed payout that covered about 60% of the cost. Since their grids covered 100% of the smallest r-tuples thus covering a significant portion of (r+1)-tuples which paid out substantially more, frequently their payout was out enough to turn a "profit" thus sustataining the pool without additional funds. Over a couple of years, the scheme won many larger payouts (but not a jackpot) until the grid price was doubled after which the group dissolved.