Best Known (69−44, 69, s)-Nets in Base 128
(69−44, 69, 321)-Net over F128 — Constructive and digital
Digital (25, 69, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 22, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (3, 47, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (0, 22, 129)-net over F128, using
(69−44, 69, 513)-Net over F128 — Digital
Digital (25, 69, 513)-net over F128, using
- t-expansion [i] based on digital (24, 69, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(69−44, 69, 289741)-Net in Base 128 — Upper bound on s
There is no (25, 69, 289742)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 24 975787 872254 247742 420389 346286 591849 125570 485902 470326 575662 375959 543254 514695 447769 971202 466171 824136 908401 527999 375018 388041 378828 120950 925008 > 12869 [i]