Best Known (154−53, 154, s)-Nets in Base 8
(154−53, 154, 389)-Net over F8 — Constructive and digital
Digital (101, 154, 389)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 34, 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 (67, 120, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 60, 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, 60, 177)-net over F64, using
- digital (8, 34, 35)-net over F8, using
(154−53, 154, 576)-Net in Base 8 — Constructive
(101, 154, 576)-net in base 8, using
- 6 times m-reduction [i] based on (101, 160, 576)-net in base 8, using
- trace code for nets [i] based on (21, 80, 288)-net in base 64, using
- 4 times m-reduction [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
- 4 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- trace code for nets [i] based on (21, 80, 288)-net in base 64, using
(154−53, 154, 1392)-Net over F8 — Digital
Digital (101, 154, 1392)-net over F8, using
(154−53, 154, 310820)-Net in Base 8 — Upper bound on s
There is no (101, 154, 310821)-net in base 8, because
- 1 times m-reduction [i] would yield (101, 153, 310821)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1 488634 968596 741261 772103 958157 632651 597474 745454 920639 198909 765249 733378 177832 233178 002080 016122 769035 236514 111404 440961 471707 173779 519336 > 8153 [i]