Best Known (61−29, 61, s)-Nets in Base 8
(61−29, 61, 160)-Net over F8 — Constructive and digital
Digital (32, 61, 160)-net over F8, using
- 1 times m-reduction [i] based on digital (32, 62, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 31, 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, 31, 80)-net over F64, using
(61−29, 61, 162)-Net over F8 — Digital
Digital (32, 61, 162)-net over F8, using
- 1 times m-reduction [i] based on digital (32, 62, 162)-net over F8, using
- trace code for nets [i] based on digital (1, 31, 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, 31, 81)-net over F64, using
(61−29, 61, 6399)-Net in Base 8 — Upper bound on s
There is no (32, 61, 6400)-net in base 8, because
- 1 times m-reduction [i] would yield (32, 60, 6400)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1 533028 570018 562803 410482 905350 155699 244360 471220 166881 > 860 [i]