Best Known (51−43, 51, s)-Nets in Base 27
(51−43, 51, 84)-Net over F27 — Constructive and digital
Digital (8, 51, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
(51−43, 51, 92)-Net over F27 — Digital
Digital (8, 51, 92)-net over F27, using
- net from sequence [i] based on digital (8, 91)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 92, using
(51−43, 51, 843)-Net in Base 27 — Upper bound on s
There is no (8, 51, 844)-net in base 27, because
- 1 times m-reduction [i] would yield (8, 50, 844)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 375837 872855 218437 460089 570503 367384 642310 451988 504689 357478 379937 678745 > 2750 [i]