Best Known (103−59, 103, s)-Nets in Base 7
(103−59, 103, 45)-Net over F7 — Constructive and digital
Digital (44, 103, 45)-net over F7, using
- net from sequence [i] based on digital (44, 44)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 44)-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, 44)-sequence over F49, using
(103−59, 103, 105)-Net over F7 — Digital
Digital (44, 103, 105)-net over F7, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
(103−59, 103, 1806)-Net in Base 7 — Upper bound on s
There is no (44, 103, 1807)-net in base 7, because
- 1 times m-reduction [i] would yield (44, 102, 1807)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 159 144522 399547 331866 204878 412753 710779 440854 858855 981730 597558 463533 240654 791448 416307 > 7102 [i]