Best Known (57, 57+35, s)-Nets in Base 8
(57, 57+35, 354)-Net over F8 — Constructive and digital
Digital (57, 92, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (57, 100, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 50, 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, 50, 177)-net over F64, using
(57, 57+35, 384)-Net in Base 8 — Constructive
(57, 92, 384)-net in base 8, using
- 2 times m-reduction [i] based on (57, 94, 384)-net in base 8, using
- trace code for nets [i] based on (10, 47, 192)-net in base 64, using
- 2 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 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, 42, 192)-net over F128, using
- 2 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- trace code for nets [i] based on (10, 47, 192)-net in base 64, using
(57, 57+35, 554)-Net over F8 — Digital
Digital (57, 92, 554)-net over F8, using
(57, 57+35, 69979)-Net in Base 8 — Upper bound on s
There is no (57, 92, 69980)-net in base 8, because
- 1 times m-reduction [i] would yield (57, 91, 69980)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 15179 421189 005040 104405 041346 534351 940119 322632 236179 635764 651478 550065 799612 197287 > 891 [i]