Best Known (86−47, 86, s)-Nets in Base 7
(86−47, 86, 40)-Net over F7 — Constructive and digital
Digital (39, 86, 40)-net over F7, using
- net from sequence [i] based on digital (39, 39)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 39)-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, 39)-sequence over F49, using
(86−47, 86, 96)-Net over F7 — Digital
Digital (39, 86, 96)-net over F7, using
- t-expansion [i] based on digital (33, 86, 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
(86−47, 86, 2072)-Net in Base 7 — Upper bound on s
There is no (39, 86, 2073)-net in base 7, because
- 1 times m-reduction [i] would yield (39, 85, 2073)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 688375 978531 038474 567084 033281 950721 942660 307685 496657 644834 256067 969463 > 785 [i]