Best Known (71, 71+30, s)-Nets in Base 8
(71, 71+30, 402)-Net over F8 — Constructive and digital
Digital (71, 101, 402)-net over F8, using
- 1 times m-reduction [i] based on digital (71, 102, 402)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 26, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- digital (45, 76, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 38, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 38, 177)-net over F64, using
- digital (11, 26, 48)-net over F8, using
- (u, u+v)-construction [i] based on
(71, 71+30, 576)-Net in Base 8 — Constructive
(71, 101, 576)-net in base 8, using
- 7 times m-reduction [i] based on (71, 108, 576)-net in base 8, using
- trace code for nets [i] based on (17, 54, 288)-net in base 64, using
- 2 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- 2 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- trace code for nets [i] based on (17, 54, 288)-net in base 64, using
(71, 71+30, 2344)-Net over F8 — Digital
Digital (71, 101, 2344)-net over F8, using
(71, 71+30, 1105276)-Net in Base 8 — Upper bound on s
There is no (71, 101, 1105277)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 16 296407 187144 157561 523647 300154 974778 175612 008657 068644 630907 082373 679182 547459 564692 028912 > 8101 [i]