Best Known (65, 65+42, s)-Nets in Base 8
(65, 65+42, 354)-Net over F8 — Constructive and digital
Digital (65, 107, 354)-net over F8, using
- 9 times m-reduction [i] based on digital (65, 116, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 58, 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, 58, 177)-net over F64, using
(65, 65+42, 384)-Net in Base 8 — Constructive
(65, 107, 384)-net in base 8, using
- 1 times m-reduction [i] based on (65, 108, 384)-net in base 8, using
- trace code for nets [i] based on (11, 54, 192)-net in base 64, using
- 2 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 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, 48, 192)-net over F128, using
- 2 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- trace code for nets [i] based on (11, 54, 192)-net in base 64, using
(65, 65+42, 536)-Net over F8 — Digital
Digital (65, 107, 536)-net over F8, using
(65, 65+42, 49515)-Net in Base 8 — Upper bound on s
There is no (65, 107, 49516)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 4 273320 677952 797189 623512 008681 627823 929747 416495 957053 705054 827706 587074 920076 385329 951399 114324 > 8107 [i]