Best Known (77−28, 77, s)-Nets in Base 8
(77−28, 77, 354)-Net over F8 — Constructive and digital
Digital (49, 77, 354)-net over F8, using
- 7 times m-reduction [i] based on digital (49, 84, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 42, 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, 42, 177)-net over F64, using
(77−28, 77, 514)-Net in Base 8 — Constructive
(49, 77, 514)-net in base 8, using
- 1 times m-reduction [i] based on (49, 78, 514)-net in base 8, using
- trace code for nets [i] based on (10, 39, 257)-net in base 64, using
- 1 times m-reduction [i] based on (10, 40, 257)-net in base 64, using
- base change [i] based on digital (0, 30, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 30, 257)-net over F256, using
- 1 times m-reduction [i] based on (10, 40, 257)-net in base 64, using
- trace code for nets [i] based on (10, 39, 257)-net in base 64, using
(77−28, 77, 601)-Net over F8 — Digital
Digital (49, 77, 601)-net over F8, using
(77−28, 77, 80040)-Net in Base 8 — Upper bound on s
There is no (49, 77, 80041)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3451 317525 414015 845459 208462 459851 940976 809449 463539 241448 395569 170032 > 877 [i]