Best Known (27, 72, s)-Nets in Base 64
(27, 72, 193)-Net over F64 — Constructive and digital
Digital (27, 72, 193)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 22, 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
- digital (5, 50, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- digital (0, 22, 65)-net over F64, using
(27, 72, 288)-Net in Base 64 — Constructive
(27, 72, 288)-net in base 64, using
- t-expansion [i] based on (22, 72, 288)-net in base 64, using
- 19 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 19 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(27, 72, 425)-Net over F64 — Digital
Digital (27, 72, 425)-net over F64, using
- t-expansion [i] based on digital (26, 72, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
(27, 72, 513)-Net in Base 64
(27, 72, 513)-net in base 64, using
- 4 times m-reduction [i] based on (27, 76, 513)-net in base 64, using
- base change [i] based on digital (8, 57, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 57, 513)-net over F256, using
(27, 72, 96939)-Net in Base 64 — Upper bound on s
There is no (27, 72, 96940)-net in base 64, because
- 1 times m-reduction [i] would yield (27, 71, 96940)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 173 324938 924723 680325 657028 435254 611704 707594 286518 682193 503989 614233 186169 820515 902248 788119 159869 588317 919201 325317 979719 841236 > 6471 [i]