Best Known (96−29, 96, s)-Nets in Base 8
(96−29, 96, 400)-Net over F8 — Constructive and digital
Digital (67, 96, 400)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 24, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (43, 72, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 36, 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, 36, 177)-net over F64, using
- digital (10, 24, 46)-net over F8, using
(96−29, 96, 576)-Net in Base 8 — Constructive
(67, 96, 576)-net in base 8, using
- t-expansion [i] based on (65, 96, 576)-net in base 8, using
- 2 times m-reduction [i] based on (65, 98, 576)-net in base 8, using
- trace code for nets [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 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, 42, 288)-net over F128, using
- trace code for nets [i] based on (16, 49, 288)-net in base 64, using
- 2 times m-reduction [i] based on (65, 98, 576)-net in base 8, using
(96−29, 96, 2029)-Net over F8 — Digital
Digital (67, 96, 2029)-net over F8, using
(96−29, 96, 1160024)-Net in Base 8 — Upper bound on s
There is no (67, 96, 1160025)-net in base 8, because
- 1 times m-reduction [i] would yield (67, 95, 1160025)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 62 165816 825763 739992 772567 762547 333066 921072 911128 790732 464875 910093 382002 431593 886856 > 895 [i]