Best Known (47, 100, s)-Nets in Base 27
(47, 100, 190)-Net over F27 — Constructive and digital
Digital (47, 100, 190)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 36, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (11, 64, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- digital (10, 36, 94)-net over F27, using
(47, 100, 370)-Net in Base 27 — Constructive
(47, 100, 370)-net in base 27, using
- t-expansion [i] based on (43, 100, 370)-net in base 27, using
- 8 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- 8 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(47, 100, 437)-Net over F27 — Digital
Digital (47, 100, 437)-net over F27, using
(47, 100, 114409)-Net in Base 27 — Upper bound on s
There is no (47, 100, 114410)-net in base 27, because
- 1 times m-reduction [i] would yield (47, 99, 114410)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 5070 886733 796357 799023 348623 357654 095482 179059 125771 965311 173205 861760 414204 594446 060557 597191 392458 764783 042092 829778 928967 898698 925966 464373 > 2799 [i]