Best Known (161−56, 161, s)-Nets in Base 3
(161−56, 161, 156)-Net over F3 — Constructive and digital
Digital (105, 161, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (105, 166, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 83, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 83, 78)-net over F9, using
(161−56, 161, 233)-Net over F3 — Digital
Digital (105, 161, 233)-net over F3, using
(161−56, 161, 3101)-Net in Base 3 — Upper bound on s
There is no (105, 161, 3102)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 65706 332217 289367 930940 950631 839849 643815 204630 101947 952882 239552 416537 611641 > 3161 [i]