Best Known (41, 41+14, s)-Nets in Base 5
(41, 41+14, 258)-Net over F5 — Constructive and digital
Digital (41, 55, 258)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 6)-net over F5, using
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- digital (34, 48, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 24, 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, 24, 126)-net over F25, using
- digital (0, 7, 6)-net over F5, using
(41, 41+14, 1562)-Net over F5 — Digital
Digital (41, 55, 1562)-net over F5, using
(41, 41+14, 262275)-Net in Base 5 — Upper bound on s
There is no (41, 55, 262276)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 277 558365 030910 927588 300468 920305 985425 > 555 [i]