Best Known (103, 157, s)-Nets in Base 8
(103, 157, 389)-Net over F8 — Constructive and digital
Digital (103, 157, 389)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 35, 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 (68, 122, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 61, 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, 61, 177)-net over F64, using
- digital (8, 35, 35)-net over F8, using
(103, 157, 576)-Net in Base 8 — Constructive
(103, 157, 576)-net in base 8, using
- 7 times m-reduction [i] based on (103, 164, 576)-net in base 8, using
- trace code for nets [i] based on (21, 82, 288)-net in base 64, using
- 2 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
- 2 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- trace code for nets [i] based on (21, 82, 288)-net in base 64, using
(103, 157, 1419)-Net over F8 — Digital
Digital (103, 157, 1419)-net over F8, using
(103, 157, 278345)-Net in Base 8 — Upper bound on s
There is no (103, 157, 278346)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 6097 741146 018734 868818 199039 037337 981055 493984 663063 530782 236072 659241 630000 999109 802908 492361 919612 704531 660586 357648 266793 058438 096251 646496 > 8157 [i]