Best Known (106−40, 106, s)-Nets in Base 8
(106−40, 106, 354)-Net over F8 — Constructive and digital
Digital (66, 106, 354)-net over F8, using
- 12 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
(106−40, 106, 432)-Net in Base 8 — Constructive
(66, 106, 432)-net in base 8, using
- trace code for nets [i] based on (13, 53, 216)-net in base 64, using
- 3 times m-reduction [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
- 3 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
(106−40, 106, 646)-Net over F8 — Digital
Digital (66, 106, 646)-net over F8, using
(106−40, 106, 72528)-Net in Base 8 — Upper bound on s
There is no (66, 106, 72529)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 534010 297171 216435 145218 258990 807763 380285 511695 695331 833541 481162 817446 186640 424844 308062 665776 > 8106 [i]