Best Known (103−60, 103, s)-Nets in Base 7
(103−60, 103, 44)-Net over F7 — Constructive and digital
Digital (43, 103, 44)-net over F7, using
- net from sequence [i] based on digital (43, 43)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 43)-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, 43)-sequence over F49, using
(103−60, 103, 105)-Net over F7 — Digital
Digital (43, 103, 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
(103−60, 103, 1580)-Net in Base 7 — Upper bound on s
There is no (43, 103, 1581)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 1116 684086 125093 461799 366809 857468 824261 577140 962401 010310 890819 083316 919958 334086 119465 > 7103 [i]