Best Known (56, 56+50, s)-Nets in Base 3
(56, 56+50, 56)-Net over F3 — Constructive and digital
Digital (56, 106, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 53, 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
(56, 56+50, 70)-Net over F3 — Digital
Digital (56, 106, 70)-net over F3, using
(56, 56+50, 512)-Net in Base 3 — Upper bound on s
There is no (56, 106, 513)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 384 904334 386812 622507 015549 805706 661793 107948 408483 > 3106 [i]