Best Known (118−56, 118, s)-Nets in Base 3
(118−56, 118, 56)-Net over F3 — Constructive and digital
Digital (62, 118, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 59, 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
(118−56, 118, 75)-Net over F3 — Digital
Digital (62, 118, 75)-net over F3, using
(118−56, 118, 552)-Net in Base 3 — Upper bound on s
There is no (62, 118, 553)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 208 944468 263219 974694 750885 102195 874081 454631 956498 570737 > 3118 [i]