Best Known (164−57, 164, s)-Nets in Base 8
(164−57, 164, 389)-Net over F8 — Constructive and digital
Digital (107, 164, 389)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 36, 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 (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 (8, 36, 35)-net over F8, using
(164−57, 164, 576)-Net in Base 8 — Constructive
(107, 164, 576)-net in base 8, using
- t-expansion [i] based on (105, 164, 576)-net in base 8, using
- 4 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
- 4 times m-reduction [i] based on (105, 168, 576)-net in base 8, using
(164−57, 164, 1397)-Net over F8 — Digital
Digital (107, 164, 1397)-net over F8, using
(164−57, 164, 291846)-Net in Base 8 — Upper bound on s
There is no (107, 164, 291847)-net in base 8, because
- 1 times m-reduction [i] would yield (107, 163, 291847)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1598 379724 485381 770506 171768 745278 641754 220216 193517 957452 108438 232545 881942 413648 785393 003267 997530 389245 677251 515940 660594 939518 535373 292512 198784 > 8163 [i]