Best Known (25, 25+38, s)-Nets in Base 64
(25, 25+38, 208)-Net over F64 — Constructive and digital
Digital (25, 63, 208)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 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, 41, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64 (see above)
- digital (3, 22, 104)-net over F64, using
(25, 25+38, 288)-Net in Base 64 — Constructive
(25, 63, 288)-net in base 64, using
- t-expansion [i] based on (22, 63, 288)-net in base 64, using
- 28 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
- 28 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(25, 25+38, 408)-Net over F64 — Digital
Digital (25, 63, 408)-net over F64, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 25 and N(F) ≥ 408, using
(25, 25+38, 513)-Net in Base 64
(25, 63, 513)-net in base 64, using
- 5 times m-reduction [i] based on (25, 68, 513)-net in base 64, using
- base change [i] based on digital (8, 51, 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, 51, 513)-net over F256, using
(25, 25+38, 122674)-Net in Base 64 — Upper bound on s
There is no (25, 63, 122675)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 615696 538715 528555 217358 390748 081829 953144 912330 885299 035690 564775 288574 996436 420992 962400 112495 351327 810566 758816 > 6463 [i]