Best Known (19, 19+31, s)-Nets in Base 64
(19, 19+31, 184)-Net over F64 — Constructive and digital
Digital (19, 50, 184)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 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, 34, 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, 16, 80)-net over F64, using
(19, 19+31, 288)-Net in Base 64 — Constructive
(19, 50, 288)-net in base 64, using
- 20 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
(19, 19+31, 315)-Net over F64 — Digital
Digital (19, 50, 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
(19, 19+31, 321)-Net in Base 64
(19, 50, 321)-net in base 64, using
- 18 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
(19, 19+31, 81016)-Net in Base 64 — Upper bound on s
There is no (19, 50, 81017)-net in base 64, because
- 1 times m-reduction [i] would yield (19, 49, 81017)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 31829 730229 316607 093957 257200 819494 101912 424338 185788 228357 147337 732557 443919 300322 854832 > 6449 [i]