Best Known (81−45, 81, s)-Nets in Base 7
(81−45, 81, 37)-Net over F7 — Constructive and digital
Digital (36, 81, 37)-net over F7, using
- net from sequence [i] based on digital (36, 36)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 36)-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, 36)-sequence over F49, using
(81−45, 81, 96)-Net over F7 — Digital
Digital (36, 81, 96)-net over F7, using
- t-expansion [i] based on digital (33, 81, 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
(81−45, 81, 1771)-Net in Base 7 — Upper bound on s
There is no (36, 81, 1772)-net in base 7, because
- 1 times m-reduction [i] would yield (36, 80, 1772)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 40 799078 822140 385574 399904 520553 811507 816988 404316 938770 752246 076073 > 780 [i]