To compute one test coefficient, enumerate T subset S_i, evaluate the listed integer lift on 1_T, and form its ell=n+1 retained coefficients modulo 2^(n+1). Each term has polynomial cost; there are at most 2^{|S_i|}<=2^{k lambda^c} terms. Process one test at a time and multiply the results for its group. Thus a test-group entry costs 2^{lambda^{O_(k,c)(1)}} bit operations and polynomial space. Variable-group entries and invalid-index checks are polynomial-time. Graphs, arrays and entry procedures have polynomial-size descriptions; no full multivariate coefficient table is stored.