Best Known (71−38, 71, s)-Nets in Base 9
(71−38, 71, 81)-Net over F9 — Constructive and digital
Digital (33, 71, 81)-net over F9, using
- t-expansion [i] based on digital (32, 71, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(71−38, 71, 88)-Net in Base 9 — Constructive
(33, 71, 88)-net in base 9, using
- 1 times m-reduction [i] based on (33, 72, 88)-net in base 9, using
- base change [i] based on digital (9, 48, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- base change [i] based on digital (9, 48, 88)-net over F27, using
(71−38, 71, 128)-Net over F9 — Digital
Digital (33, 71, 128)-net over F9, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
(71−38, 71, 3635)-Net in Base 9 — Upper bound on s
There is no (33, 71, 3636)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 56 392177 474977 831494 799919 028637 537276 227194 328896 491872 692375 098465 > 971 [i]