Best Known (64, 106, s)-Nets in Base 8
(64, 106, 354)-Net over F8 — Constructive and digital
Digital (64, 106, 354)-net over F8, using
- 8 times m-reduction [i] based on digital (64, 114, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 57, 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, 57, 177)-net over F64, using
(64, 106, 384)-Net in Base 8 — Constructive
(64, 106, 384)-net in base 8, using
- trace code for nets [i] based on (11, 53, 192)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
(64, 106, 508)-Net over F8 — Digital
Digital (64, 106, 508)-net over F8, using
(64, 106, 44845)-Net in Base 8 — Upper bound on s
There is no (64, 106, 44846)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 534018 175810 688149 862306 424978 650579 282643 942588 167634 804631 160755 599530 989265 637461 464260 766858 > 8106 [i]