Order the N incidences and list size-d subsets lexicographically by their increasing element lists. At the first undecided incidence, with R positions remaining and t still needed, binom(R-1,t-1) completions contain that incidence. If the index is smaller, include it; otherwise subtract that count and omit it. Continue, using the forced cases t=0 or t=R directly. Binomial counts can be computed by integer recurrences. They have at most O(N) bits because there are at most 2^N subsets. Decoding takes polynomial time and space in N, not time proportional to the number of subsets.