Best Known (68−33, 68, s)-Nets in Base 8
(68−33, 68, 160)-Net over F8 — Constructive and digital
Digital (35, 68, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 34, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(68−33, 68, 162)-Net over F8 — Digital
Digital (35, 68, 162)-net over F8, using
- trace code for nets [i] based on digital (1, 34, 81)-net over F64, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
(68−33, 68, 5866)-Net in Base 8 — Upper bound on s
There is no (35, 68, 5867)-net in base 8, because
- 1 times m-reduction [i] would yield (35, 67, 5867)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 3 214997 617999 545617 510203 428712 277427 124929 140982 200630 934270 > 867 [i]