Best Known (31−12, 31, s)-Nets in Base 3
(31−12, 31, 56)-Net over F3 — Constructive and digital
Digital (19, 31, 56)-net over F3, using
- 1 times m-reduction [i] based on digital (19, 32, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 16, 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, 16, 28)-net over F9, using
(31−12, 31, 431)-Net in Base 3 — Upper bound on s
There is no (19, 31, 432)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 623 079871 578145 > 331 [i]