Best Known (51−30, 51, s)-Nets in Base 64
(51−30, 51, 208)-Net over F64 — Constructive and digital
Digital (21, 51, 208)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 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 (3, 33, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64 (see above)
- digital (3, 18, 104)-net over F64, using
(51−30, 51, 288)-Net in Base 64 — Constructive
(21, 51, 288)-net in base 64, using
- 33 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
(51−30, 51, 342)-Net over F64 — Digital
Digital (21, 51, 342)-net over F64, using
- t-expansion [i] based on digital (20, 51, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
(51−30, 51, 513)-Net in Base 64
(21, 51, 513)-net in base 64, using
- 1 times m-reduction [i] based on (21, 52, 513)-net in base 64, using
- base change [i] based on digital (8, 39, 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, 39, 513)-net over F256, using
(51−30, 51, 141063)-Net in Base 64 — Upper bound on s
There is no (21, 51, 141064)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 130 372440 540857 805192 382907 795553 327018 412899 587361 133753 887101 932112 245207 229392 371880 224160 > 6451 [i]