Best Known (69, 111, s)-Nets in Base 8
(69, 111, 354)-Net over F8 — Constructive and digital
Digital (69, 111, 354)-net over F8, using
- 13 times m-reduction [i] based on digital (69, 124, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 62, 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, 62, 177)-net over F64, using
(69, 111, 432)-Net in Base 8 — Constructive
(69, 111, 432)-net in base 8, using
- 1 times m-reduction [i] based on (69, 112, 432)-net in base 8, using
- trace code for nets [i] based on (13, 56, 216)-net in base 64, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- trace code for nets [i] based on (13, 56, 216)-net in base 64, using
(69, 111, 663)-Net over F8 — Digital
Digital (69, 111, 663)-net over F8, using
(69, 111, 73585)-Net in Base 8 — Upper bound on s
There is no (69, 111, 73586)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 17499 475207 296728 003279 698970 220305 338874 620552 923115 995566 158505 187799 945483 233962 993778 535715 008072 > 8111 [i]