Best Known (26, 26+35, s)-Nets in Base 64
(26, 26+35, 257)-Net over F64 — Constructive and digital
Digital (26, 61, 257)-net over F64, using
- 1 times m-reduction [i] based on digital (26, 62, 257)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 19, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (7, 43, 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
- digital (1, 19, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(26, 26+35, 288)-Net in Base 64 — Constructive
(26, 61, 288)-net in base 64, using
- t-expansion [i] based on (22, 61, 288)-net in base 64, using
- 30 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
- 30 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(26, 26+35, 425)-Net over F64 — Digital
Digital (26, 61, 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
(26, 26+35, 513)-Net in Base 64
(26, 61, 513)-net in base 64, using
- 11 times m-reduction [i] based on (26, 72, 513)-net in base 64, using
- base change [i] based on digital (8, 54, 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, 54, 513)-net over F256, using
(26, 26+35, 269987)-Net in Base 64 — Upper bound on s
There is no (26, 61, 269988)-net in base 64, because
- 1 times m-reduction [i] would yield (26, 60, 269988)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 2 348566 246407 401818 188567 654984 725669 680337 302983 298839 037544 960578 638371 862732 632451 739232 192201 648538 457750 > 6460 [i]