Best Known (75, 75+28, s)-Nets in Base 4
(75, 75+28, 384)-Net over F4 — Constructive and digital
Digital (75, 103, 384)-net over F4, using
- 2 times m-reduction [i] based on digital (75, 105, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 35, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 35, 128)-net over F64, using
(75, 75+28, 450)-Net in Base 4 — Constructive
(75, 103, 450)-net in base 4, using
- 41 times duplication [i] based on (74, 102, 450)-net in base 4, using
- trace code for nets [i] based on (6, 34, 150)-net in base 64, using
- 1 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 30, 150)-net over F128, using
- 1 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- trace code for nets [i] based on (6, 34, 150)-net in base 64, using
(75, 75+28, 734)-Net over F4 — Digital
Digital (75, 103, 734)-net over F4, using
(75, 75+28, 54161)-Net in Base 4 — Upper bound on s
There is no (75, 103, 54162)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 102 865142 648441 532269 756131 495867 251973 527115 794999 784012 570312 > 4103 [i]