Best Known (27, 27+46, s)-Nets in Base 64
(27, 27+46, 184)-Net over F64 — Constructive and digital
Digital (27, 73, 184)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 24, 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 (3, 49, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (1, 24, 80)-net over F64, using
(27, 27+46, 288)-Net in Base 64 — Constructive
(27, 73, 288)-net in base 64, using
- t-expansion [i] based on (22, 73, 288)-net in base 64, using
- 18 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
- 18 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(27, 27+46, 425)-Net over F64 — Digital
Digital (27, 73, 425)-net over F64, using
- t-expansion [i] based on digital (26, 73, 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, 27+46, 513)-Net in Base 64
(27, 73, 513)-net in base 64, using
- 3 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, 27+46, 80856)-Net in Base 64 — Upper bound on s
There is no (27, 73, 80857)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 709982 132100 350178 953838 870926 841069 938363 875998 778610 595742 976709 435038 554389 590210 529580 732814 343546 658362 929878 475374 162290 137032 > 6473 [i]