Best Known (22, 22+31, s)-Nets in Base 64
(22, 22+31, 242)-Net over F64 — Constructive and digital
Digital (22, 53, 242)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 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 (7, 38, 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 (0, 15, 65)-net over F64, using
(22, 22+31, 288)-Net in Base 64 — Constructive
(22, 53, 288)-net in base 64, using
- 38 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
(22, 22+31, 342)-Net over F64 — Digital
Digital (22, 53, 342)-net over F64, using
- t-expansion [i] based on digital (20, 53, 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
(22, 22+31, 513)-Net in Base 64
(22, 53, 513)-net in base 64, using
- 3 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
(22, 22+31, 186137)-Net in Base 64 — Upper bound on s
There is no (22, 53, 186138)-net in base 64, because
- 1 times m-reduction [i] would yield (22, 52, 186138)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 8344 255418 664765 059067 094500 414098 902917 516133 769823 598025 213777 036785 790876 801866 366817 857000 > 6452 [i]