Best Known (20, 20+17, s)-Nets in Base 8
(20, 20+17, 160)-Net over F8 — Constructive and digital
Digital (20, 37, 160)-net over F8, using
- 1 times m-reduction [i] based on digital (20, 38, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 19, 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
- trace code for nets [i] based on digital (1, 19, 80)-net over F64, using
(20, 20+17, 162)-Net over F8 — Digital
Digital (20, 37, 162)-net over F8, using
- 1 times m-reduction [i] based on digital (20, 38, 162)-net over F8, using
- trace code for nets [i] based on digital (1, 19, 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
- trace code for nets [i] based on digital (1, 19, 81)-net over F64, using
(20, 20+17, 6225)-Net in Base 8 — Upper bound on s
There is no (20, 37, 6226)-net in base 8, because
- 1 times m-reduction [i] would yield (20, 36, 6226)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 324 732695 220774 743506 943219 217646 > 836 [i]