Best Known (37, 37+47, s)-Nets in Base 7
(37, 37+47, 38)-Net over F7 — Constructive and digital
Digital (37, 84, 38)-net over F7, using
- net from sequence [i] based on digital (37, 37)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 37)-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, 37)-sequence over F49, using
(37, 37+47, 96)-Net over F7 — Digital
Digital (37, 84, 96)-net over F7, using
- t-expansion [i] based on digital (33, 84, 96)-net over F7, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 33 and N(F) ≥ 96, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
(37, 37+47, 1747)-Net in Base 7 — Upper bound on s
There is no (37, 84, 1748)-net in base 7, because
- 1 times m-reduction [i] would yield (37, 83, 1748)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 14048 021168 012843 011770 308846 766405 444982 532870 925998 246909 011786 696033 > 783 [i]