Best Known (43, 43+35, s)-Nets in Base 27
(43, 43+35, 210)-Net over F27 — Constructive and digital
Digital (43, 78, 210)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 15, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 21, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (7, 42, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 15, 64)-net over F27, using
(43, 43+35, 370)-Net in Base 27 — Constructive
(43, 78, 370)-net in base 27, using
- 30 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
(43, 43+35, 1018)-Net over F27 — Digital
Digital (43, 78, 1018)-net over F27, using
(43, 43+35, 839852)-Net in Base 27 — Upper bound on s
There is no (43, 78, 839853)-net in base 27, because
- 1 times m-reduction [i] would yield (43, 77, 839853)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 164 062829 826405 216973 822491 599948 807680 484324 577873 681580 949730 719581 619921 698896 870623 832317 059973 483265 626579 > 2777 [i]