Best Known (59, 59+36, s)-Nets in Base 8
(59, 59+36, 354)-Net over F8 — Constructive and digital
Digital (59, 95, 354)-net over F8, using
- 9 times m-reduction [i] based on digital (59, 104, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 52, 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, 52, 177)-net over F64, using
(59, 59+36, 384)-Net in Base 8 — Constructive
(59, 95, 384)-net in base 8, using
- 3 times m-reduction [i] based on (59, 98, 384)-net in base 8, using
- trace code for nets [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
- trace code for nets [i] based on (10, 49, 192)-net in base 64, using
(59, 59+36, 579)-Net over F8 — Digital
Digital (59, 95, 579)-net over F8, using
(59, 59+36, 62988)-Net in Base 8 — Upper bound on s
There is no (59, 95, 62989)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 62 167353 215240 163983 535923 642422 380089 818725 817806 576018 543228 086995 379276 768851 464640 > 895 [i]