Best Known (44, 44+43, s)-Nets in Base 8
(44, 44+43, 130)-Net over F8 — Constructive and digital
Digital (44, 87, 130)-net over F8, using
- 1 times m-reduction [i] based on digital (44, 88, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 44, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 44, 65)-net over F64, using
(44, 44+43, 164)-Net over F8 — Digital
Digital (44, 87, 164)-net over F8, using
(44, 44+43, 6178)-Net in Base 8 — Upper bound on s
There is no (44, 87, 6179)-net in base 8, because
- 1 times m-reduction [i] would yield (44, 86, 6179)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 464678 227394 766510 529342 426780 598705 028565 251279 799231 690900 293163 066799 826864 > 886 [i]