Best Known (103−35, 103, s)-Nets in Base 8
(103−35, 103, 371)-Net over F8 — Constructive and digital
Digital (68, 103, 371)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 19, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (49, 84, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 42, 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, 42, 177)-net over F64, using
- digital (2, 19, 17)-net over F8, using
(103−35, 103, 520)-Net in Base 8 — Constructive
(68, 103, 520)-net in base 8, using
- 1 times m-reduction [i] based on (68, 104, 520)-net in base 8, using
- base change [i] based on digital (42, 78, 520)-net over F16, using
- trace code for nets [i] based on digital (3, 39, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- trace code for nets [i] based on digital (3, 39, 260)-net over F256, using
- base change [i] based on digital (42, 78, 520)-net over F16, using
(103−35, 103, 1069)-Net over F8 — Digital
Digital (68, 103, 1069)-net over F8, using
(103−35, 103, 268763)-Net in Base 8 — Upper bound on s
There is no (68, 103, 268764)-net in base 8, because
- 1 times m-reduction [i] would yield (68, 102, 268764)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 130 374682 553158 899484 464719 857234 808372 053569 048214 121703 999875 095131 365787 771385 561880 109007 > 8102 [i]