Best Known (27, 47, s)-Nets in Base 3
(27, 47, 56)-Net over F3 — Constructive and digital
Digital (27, 47, 56)-net over F3, using
- 1 times m-reduction [i] based on digital (27, 48, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 24, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- trace code for nets [i] based on digital (3, 24, 28)-net over F9, using
(27, 47, 386)-Net in Base 3 — Upper bound on s
There is no (27, 47, 387)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 27035 504852 212563 425877 > 347 [i]