Best Known (55−36, 55, s)-Nets in Base 64
(55−36, 55, 177)-Net over F64 — Constructive and digital
Digital (19, 55, 177)-net over F64, using
- t-expansion [i] based on digital (7, 55, 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
(55−36, 55, 288)-Net in Base 64 — Constructive
(19, 55, 288)-net in base 64, using
- 15 times m-reduction [i] based on (19, 70, 288)-net in base 64, using
- base change [i] based on digital (9, 60, 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, 60, 288)-net over F128, using
(55−36, 55, 315)-Net over F64 — Digital
Digital (19, 55, 315)-net over F64, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 19 and N(F) ≥ 315, using
(55−36, 55, 321)-Net in Base 64
(19, 55, 321)-net in base 64, using
- 13 times m-reduction [i] based on (19, 68, 321)-net in base 64, using
- base change [i] based on digital (2, 51, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 51, 321)-net over F256, using
(55−36, 55, 39589)-Net in Base 64 — Upper bound on s
There is no (19, 55, 39590)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2188 076115 476197 882493 960315 942758 332847 482538 700461 639967 196952 996828 127066 469556 469086 889777 662540 > 6455 [i]