Best Known (51, 51+24, s)-Nets in Base 7
(51, 51+24, 202)-Net over F7 — Constructive and digital
Digital (51, 75, 202)-net over F7, using
- 1 times m-reduction [i] based on digital (51, 76, 202)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (12, 24, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 12, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 12, 50)-net over F49, using
- digital (27, 52, 102)-net over F7, using
- trace code for nets [i] based on digital (1, 26, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- trace code for nets [i] based on digital (1, 26, 51)-net over F49, using
- digital (12, 24, 100)-net over F7, using
- (u, u+v)-construction [i] based on
(51, 51+24, 907)-Net over F7 — Digital
Digital (51, 75, 907)-net over F7, using
(51, 51+24, 168676)-Net in Base 7 — Upper bound on s
There is no (51, 75, 168677)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 2412 015949 431202 311043 925422 273744 443332 823307 016035 952585 407777 > 775 [i]