Best Known (57, 112, s)-Nets in Base 8
(57, 112, 160)-Net over F8 — Constructive and digital
Digital (57, 112, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 56, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(57, 112, 206)-Net over F8 — Digital
Digital (57, 112, 206)-net over F8, using
(57, 112, 8037)-Net in Base 8 — Upper bound on s
There is no (57, 112, 8038)-net in base 8, because
- 1 times m-reduction [i] would yield (57, 111, 8038)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 17547 296248 944222 344246 653760 106665 149549 313768 385826 430634 732971 219904 249784 001770 101572 429688 417560 > 8111 [i]