Best Known (35, 35+22, s)-Nets in Base 8
(35, 35+22, 256)-Net over F8 — Constructive and digital
Digital (35, 57, 256)-net over F8, using
- 3 times m-reduction [i] based on digital (35, 60, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 30, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 30, 128)-net over F64, using
(35, 35+22, 300)-Net in Base 8 — Constructive
(35, 57, 300)-net in base 8, using
- 81 times duplication [i] based on (34, 56, 300)-net in base 8, using
- t-expansion [i] based on (33, 56, 300)-net in base 8, using
- trace code for nets [i] based on (5, 28, 150)-net in base 64, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 24, 150)-net over F128, using
- trace code for nets [i] based on (5, 28, 150)-net in base 64, using
- t-expansion [i] based on (33, 56, 300)-net in base 8, using
(35, 35+22, 361)-Net over F8 — Digital
Digital (35, 57, 361)-net over F8, using
(35, 35+22, 33533)-Net in Base 8 — Upper bound on s
There is no (35, 57, 33534)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2993 627046 879444 473249 419179 142336 573056 930843 036334 > 857 [i]