Best Known (142−48, 142, s)-Nets in Base 8
(142−48, 142, 389)-Net over F8 — Constructive and digital
Digital (94, 142, 389)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 32, 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 (62, 110, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 55, 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, 55, 177)-net over F64, using
- digital (8, 32, 35)-net over F8, using
(142−48, 142, 576)-Net in Base 8 — Constructive
(94, 142, 576)-net in base 8, using
- 6 times m-reduction [i] based on (94, 148, 576)-net in base 8, using
- trace code for nets [i] based on (20, 74, 288)-net in base 64, using
- 3 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 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, 66, 288)-net over F128, using
- 3 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- trace code for nets [i] based on (20, 74, 288)-net in base 64, using
(142−48, 142, 1428)-Net over F8 — Digital
Digital (94, 142, 1428)-net over F8, using
(142−48, 142, 308692)-Net in Base 8 — Upper bound on s
There is no (94, 142, 308693)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 173 298215 286460 085619 497577 066709 374755 573245 961397 599261 970867 803158 611250 884933 037687 267505 402984 540785 475763 705472 938134 874472 > 8142 [i]