Best Known (43, 89, s)-Nets in Base 7
(43, 89, 44)-Net over F7 — Constructive and digital
Digital (43, 89, 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
(43, 89, 121)-Net over F7 — Digital
Digital (43, 89, 121)-net over F7, using
(43, 89, 2912)-Net in Base 7 — Upper bound on s
There is no (43, 89, 2913)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 1642 357215 639428 138379 158910 568209 797468 331575 853258 902777 719665 949897 991287 > 789 [i]