Best Known (50−28, 50, s)-Nets in Base 64
(50−28, 50, 257)-Net over F64 — Constructive and digital
Digital (22, 50, 257)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 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, 35, 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, 15, 80)-net over F64, using
(50−28, 50, 288)-Net in Base 64 — Constructive
(22, 50, 288)-net in base 64, using
- 41 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
(50−28, 50, 397)-Net over F64 — Digital
Digital (22, 50, 397)-net over F64, using
(50−28, 50, 513)-Net in Base 64
(22, 50, 513)-net in base 64, using
- 6 times m-reduction [i] based on (22, 56, 513)-net in base 64, using
- base change [i] based on digital (8, 42, 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, 42, 513)-net over F256, using
(50−28, 50, 270862)-Net in Base 64 — Upper bound on s
There is no (22, 50, 270863)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2 037069 342168 699877 370185 148225 464503 837028 615292 184216 920532 798726 601868 922994 489344 464833 > 6450 [i]