Best Known (55, 55+32, s)-Nets in Base 8
(55, 55+32, 354)-Net over F8 — Constructive and digital
Digital (55, 87, 354)-net over F8, using
- 9 times m-reduction [i] based on digital (55, 96, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 48, 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, 48, 177)-net over F64, using
(55, 55+32, 514)-Net in Base 8 — Constructive
(55, 87, 514)-net in base 8, using
- 1 times m-reduction [i] based on (55, 88, 514)-net in base 8, using
- base change [i] based on digital (33, 66, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 33, 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
- trace code for nets [i] based on digital (0, 33, 257)-net over F256, using
- base change [i] based on digital (33, 66, 514)-net over F16, using
(55, 55+32, 623)-Net over F8 — Digital
Digital (55, 87, 623)-net over F8, using
(55, 55+32, 79056)-Net in Base 8 — Upper bound on s
There is no (55, 87, 79057)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3 705564 309849 507500 772503 146404 181299 304904 115511 992485 231501 635226 862329 704645 > 887 [i]