Best Known (119−51, 119, s)-Nets in Base 3
(119−51, 119, 80)-Net over F3 — Constructive and digital
Digital (68, 119, 80)-net over F3, using
- 1 times m-reduction [i] based on digital (68, 120, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 60, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- trace code for nets [i] based on digital (8, 60, 40)-net over F9, using
(119−51, 119, 100)-Net over F3 — Digital
Digital (68, 119, 100)-net over F3, using
(119−51, 119, 884)-Net in Base 3 — Upper bound on s
There is no (68, 119, 885)-net in base 3, because
- 1 times m-reduction [i] would yield (68, 118, 885)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 200 412301 465501 960707 426432 798161 583378 303865 472254 419723 > 3118 [i]