Best Known (40−24, 40, s)-Nets in Base 64
(40−24, 40, 184)-Net over F64 — Constructive and digital
Digital (16, 40, 184)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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 (3, 27, 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 (1, 13, 80)-net over F64, using
(40−24, 40, 267)-Net over F64 — Digital
Digital (16, 40, 267)-net over F64, using
- net from sequence [i] based on digital (16, 266)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 16 and N(F) ≥ 267, using
(40−24, 40, 288)-Net in Base 64 — Constructive
(16, 40, 288)-net in base 64, using
- 9 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 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, 42, 288)-net over F128, using
(40−24, 40, 321)-Net in Base 64
(16, 40, 321)-net in base 64, using
- 16 times m-reduction [i] based on (16, 56, 321)-net in base 64, using
- base change [i] based on digital (2, 42, 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, 42, 321)-net over F256, using
(40−24, 40, 88022)-Net in Base 64 — Upper bound on s
There is no (16, 40, 88023)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 1 767016 155422 088411 832436 258764 377435 151780 127330 764904 909452 325607 241438 > 6440 [i]