Best Known (71−33, 71, s)-Nets in Base 2
(71−33, 71, 28)-Net over F2 — Constructive and digital
Digital (38, 71, 28)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (11, 27, 14)-net over F2, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 11 and N(F) ≥ 14, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- digital (11, 44, 14)-net over F2, using
- net from sequence [i] based on digital (11, 13)-sequence over F2 (see above)
- digital (11, 27, 14)-net over F2, using
(71−33, 71, 30)-Net over F2 — Digital
Digital (38, 71, 30)-net over F2, using
- t-expansion [i] based on digital (36, 71, 30)-net over F2, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 36 and N(F) ≥ 30, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
(71−33, 71, 107)-Net in Base 2 — Upper bound on s
There is no (38, 71, 108)-net in base 2, because
- 1 times m-reduction [i] would yield (38, 70, 108)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(270, 108, S2, 32), but
- the linear programming bound shows that M ≥ 4 297708 243581 570312 211812 843520 / 3462 071301 > 270 [i]
- extracting embedded orthogonal array [i] would yield OA(270, 108, S2, 32), but