Best Known (59−23, 59, s)-Nets in Base 8
(59−23, 59, 256)-Net over F8 — Constructive and digital
Digital (36, 59, 256)-net over F8, using
- 3 times m-reduction [i] based on digital (36, 62, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 31, 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, 31, 128)-net over F64, using
(59−23, 59, 300)-Net in Base 8 — Constructive
(36, 59, 300)-net in base 8, using
- 1 times m-reduction [i] based on (36, 60, 300)-net in base 8, using
- trace code for nets [i] based on (6, 30, 150)-net in base 64, using
- 5 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 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, 30, 150)-net over F128, using
- 5 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- trace code for nets [i] based on (6, 30, 150)-net in base 64, using
(59−23, 59, 353)-Net over F8 — Digital
Digital (36, 59, 353)-net over F8, using
(59−23, 59, 40512)-Net in Base 8 — Upper bound on s
There is no (36, 59, 40513)-net in base 8, because
- 1 times m-reduction [i] would yield (36, 58, 40513)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 23946 164241 384984 624056 481370 190827 210538 773599 603264 > 858 [i]