Best Known (64, 64+38, s)-Nets in Base 8
(64, 64+38, 354)-Net over F8 — Constructive and digital
Digital (64, 102, 354)-net over F8, using
- 12 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, 64+38, 514)-Net in Base 8 — Constructive
(64, 102, 514)-net in base 8, using
- trace code for nets [i] based on (13, 51, 257)-net in base 64, using
- 1 times m-reduction [i] based on (13, 52, 257)-net in base 64, using
- base change [i] based on digital (0, 39, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 39, 257)-net over F256, using
- 1 times m-reduction [i] based on (13, 52, 257)-net in base 64, using
(64, 64+38, 665)-Net over F8 — Digital
Digital (64, 102, 665)-net over F8, using
(64, 64+38, 79840)-Net in Base 8 — Upper bound on s
There is no (64, 102, 79841)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 130 398338 726883 342023 769989 946898 525685 328130 883304 976699 559069 598029 285230 895778 401018 303520 > 8102 [i]