Best Known (59−25, 59, s)-Nets in Base 8
(59−25, 59, 208)-Net over F8 — Constructive and digital
Digital (34, 59, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (34, 62, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 31, 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, 31, 104)-net over F64, using
(59−25, 59, 258)-Net over F8 — Digital
Digital (34, 59, 258)-net over F8, using
- 1 times m-reduction [i] based on digital (34, 60, 258)-net over F8, using
- trace code for nets [i] based on digital (4, 30, 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, 30, 129)-net over F64, using
(59−25, 59, 17499)-Net in Base 8 — Upper bound on s
There is no (34, 59, 17500)-net in base 8, because
- 1 times m-reduction [i] would yield (34, 58, 17500)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 23957 627126 967232 722106 999310 118655 788800 438825 967876 > 858 [i]