Best Known (52, 79, s)-Nets in Base 8
(52, 79, 354)-Net over F8 — Constructive and digital
Digital (52, 79, 354)-net over F8, using
- 11 times m-reduction [i] based on digital (52, 90, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 45, 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, 45, 177)-net over F64, using
(52, 79, 518)-Net in Base 8 — Constructive
(52, 79, 518)-net in base 8, using
- 1 times m-reduction [i] based on (52, 80, 518)-net in base 8, using
- base change [i] based on digital (32, 60, 518)-net over F16, using
- trace code for nets [i] based on digital (2, 30, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 30, 259)-net over F256, using
- base change [i] based on digital (32, 60, 518)-net over F16, using
(52, 79, 849)-Net over F8 — Digital
Digital (52, 79, 849)-net over F8, using
(52, 79, 212242)-Net in Base 8 — Upper bound on s
There is no (52, 79, 212243)-net in base 8, because
- 1 times m-reduction [i] would yield (52, 78, 212243)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 27608 136091 344536 796842 443669 319465 844830 335833 371257 772147 678453 321832 > 878 [i]