Best Known (75, 75+20, s)-Nets in Base 5
(75, 75+20, 408)-Net over F5 — Constructive and digital
Digital (75, 95, 408)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (25, 35, 156)-net over F5, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 5, 52)-net over F5, using
- s-reduction based on digital (2, 5, 66)-net over F5, using
- net defined by OOA [i] based on linear OOA(55, 66, F5, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(55, 66, F5, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(55, 66, F5, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
- s-reduction based on digital (2, 5, 66)-net over F5, using
- digital (5, 10, 52)-net over F5, using
- s-reduction based on digital (5, 10, 68)-net over F5, using
- digital (10, 20, 52)-net over F5, using
- trace code for nets [i] based on digital (0, 10, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- trace code for nets [i] based on digital (0, 10, 26)-net over F25, using
- digital (2, 5, 52)-net over F5, using
- generalized (u, u+v)-construction [i] based on
- digital (40, 60, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 30, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 30, 126)-net over F25, using
- digital (25, 35, 156)-net over F5, using
(75, 75+20, 6204)-Net over F5 — Digital
Digital (75, 95, 6204)-net over F5, using
(75, 75+20, 4944595)-Net in Base 5 — Upper bound on s
There is no (75, 95, 4944596)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2 524359 248433 082773 097462 364997 409276 714908 914763 055014 770476 483521 > 595 [i]