Best Known (163−57, 163, s)-Nets in Base 8
(163−57, 163, 388)-Net over F8 — Constructive and digital
Digital (106, 163, 388)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (71, 128, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 64, 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, 64, 177)-net over F64, using
- digital (7, 35, 34)-net over F8, using
(163−57, 163, 576)-Net in Base 8 — Constructive
(106, 163, 576)-net in base 8, using
- t-expansion [i] based on (105, 163, 576)-net in base 8, using
- 5 times m-reduction [i] based on (105, 168, 576)-net in base 8, using
- trace code for nets [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
- trace code for nets [i] based on (21, 84, 288)-net in base 64, using
- 5 times m-reduction [i] based on (105, 168, 576)-net in base 8, using
(163−57, 163, 1347)-Net over F8 — Digital
Digital (106, 163, 1347)-net over F8, using
(163−57, 163, 270956)-Net in Base 8 — Upper bound on s
There is no (106, 163, 270957)-net in base 8, because
- 1 times m-reduction [i] would yield (106, 162, 270957)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 199 802143 637114 689730 802395 926855 847142 595793 091509 585061 451561 866231 882561 730776 822204 945236 105770 596893 810748 374613 358164 377353 980990 257144 340974 > 8162 [i]