Best Known (22, 22+56, s)-Nets in Base 64
(22, 22+56, 177)-Net over F64 — Constructive and digital
Digital (22, 78, 177)-net over F64, using
- t-expansion [i] based on digital (7, 78, 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
(22, 22+56, 288)-Net in Base 64 — Constructive
(22, 78, 288)-net in base 64, using
- 13 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+56, 342)-Net over F64 — Digital
Digital (22, 78, 342)-net over F64, using
- t-expansion [i] based on digital (20, 78, 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+56, 19268)-Net in Base 64 — Upper bound on s
There is no (22, 78, 19269)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 762 512726 866357 201677 729106 178639 793085 833696 788455 352773 225708 400022 160059 303478 871124 160864 863675 639944 629510 854736 232675 308440 089256 049528 > 6478 [i]