Best Known (47, 106, s)-Nets in Base 7
(47, 106, 48)-Net over F7 — Constructive and digital
Digital (47, 106, 48)-net over F7, using
- net from sequence [i] based on digital (47, 47)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 47)-sequence over F49, using
- s-reduction 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]
- s-reduction based on digital (0, 49)-sequence over F49, using
- base reduction for sequences [i] based on digital (0, 47)-sequence over F49, using
(47, 106, 105)-Net over F7 — Digital
Digital (47, 106, 105)-net over F7, using
- t-expansion [i] based on digital (43, 106, 105)-net over F7, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
(47, 106, 2213)-Net in Base 7 — Upper bound on s
There is no (47, 106, 2214)-net in base 7, because
- 1 times m-reduction [i] would yield (47, 105, 2214)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 54499 629502 967495 398724 331955 492447 364520 582863 646026 822736 544104 777983 818214 915313 699565 > 7105 [i]