Best Known (71, 71+33, s)-Nets in Base 8
(71, 71+33, 389)-Net over F8 — Constructive and digital
Digital (71, 104, 389)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 24, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (47, 80, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 40, 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, 40, 177)-net over F64, using
- digital (8, 24, 35)-net over F8, using
(71, 71+33, 576)-Net in Base 8 — Constructive
(71, 104, 576)-net in base 8, using
- 4 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+33, 1589)-Net over F8 — Digital
Digital (71, 104, 1589)-net over F8, using
(71, 71+33, 632522)-Net in Base 8 — Upper bound on s
There is no (71, 104, 632523)-net in base 8, because
- 1 times m-reduction [i] would yield (71, 103, 632523)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1042 984132 878455 074513 164420 728662 897379 533968 729370 857239 233579 323071 739104 150443 635376 349212 > 8103 [i]