Best Known (28, 28+22, s)-Nets in Base 3
(28, 28+22, 56)-Net over F3 — Constructive and digital
Digital (28, 50, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 25, 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
(28, 28+22, 351)-Net in Base 3 — Upper bound on s
There is no (28, 50, 352)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 725946 004106 244853 898625 > 350 [i]