Best Known (89−40, 89, s)-Nets in Base 8
(89−40, 89, 208)-Net over F8 — Constructive and digital
Digital (49, 89, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (49, 92, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 46, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 46, 104)-net over F64, using
(89−40, 89, 258)-Net over F8 — Digital
Digital (49, 89, 258)-net over F8, using
- 1 times m-reduction [i] based on digital (49, 90, 258)-net over F8, using
- trace code for nets [i] based on digital (4, 45, 129)-net over F64, using
- net from sequence [i] based on digital (4, 128)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- net from sequence [i] based on digital (4, 128)-sequence over F64, using
- trace code for nets [i] based on digital (4, 45, 129)-net over F64, using
(89−40, 89, 12374)-Net in Base 8 — Upper bound on s
There is no (49, 89, 12375)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 237 359527 060220 873608 285080 567735 176274 722572 697790 939021 089452 155035 186377 927051 > 889 [i]