Best Known (75, 75+80, s)-Nets in Base 4
(75, 75+80, 104)-Net over F4 — Constructive and digital
Digital (75, 155, 104)-net over F4, using
- t-expansion [i] based on digital (73, 155, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(75, 75+80, 112)-Net over F4 — Digital
Digital (75, 155, 112)-net over F4, using
- t-expansion [i] based on digital (73, 155, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(75, 75+80, 1099)-Net in Base 4 — Upper bound on s
There is no (75, 155, 1100)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2159 403592 671779 502800 849447 740553 334330 660580 741566 169533 373582 248372 583435 022659 428186 451558 > 4155 [i]