Best Known (30, 30+30, s)-Nets in Base 7
(30, 30+30, 100)-Net over F7 — Constructive and digital
Digital (30, 60, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 30, 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
(30, 30+30, 102)-Net over F7 — Digital
Digital (30, 60, 102)-net over F7, using
(30, 30+30, 2560)-Net in Base 7 — Upper bound on s
There is no (30, 60, 2561)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 508 164101 319737 080417 615977 899570 321721 166667 486263 > 760 [i]