Best Known (50, 82, s)-Nets in Base 8
(50, 82, 354)-Net over F8 — Constructive and digital
Digital (50, 82, 354)-net over F8, using
- 4 times m-reduction [i] based on digital (50, 86, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 43, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 43, 177)-net over F64, using
(50, 82, 384)-Net in Base 8 — Constructive
(50, 82, 384)-net in base 8, using
- trace code for nets [i] based on (9, 41, 192)-net in base 64, using
- 1 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- 1 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
(50, 82, 450)-Net over F8 — Digital
Digital (50, 82, 450)-net over F8, using
(50, 82, 41273)-Net in Base 8 — Upper bound on s
There is no (50, 82, 41274)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 113 089208 829126 868044 845299 601972 893460 183786 241777 440534 672350 309007 214249 > 882 [i]