Best Known (66, 66+44, s)-Nets in Base 8
(66, 66+44, 354)-Net over F8 — Constructive and digital
Digital (66, 110, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (66, 118, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 59, 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, 59, 177)-net over F64, using
(66, 66+44, 384)-Net in Base 8 — Constructive
(66, 110, 384)-net in base 8, using
- trace code for nets [i] based on (11, 55, 192)-net in base 64, using
- 1 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
- 1 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
(66, 66+44, 498)-Net over F8 — Digital
Digital (66, 110, 498)-net over F8, using
(66, 66+44, 42370)-Net in Base 8 — Upper bound on s
There is no (66, 110, 42371)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2187 648772 769963 650460 427879 877375 705803 595170 890050 911858 201654 328864 551325 549350 656899 924452 233184 > 8110 [i]