Best Known (216−86, 216, s)-Nets in Base 3
(216−86, 216, 156)-Net over F3 — Constructive and digital
Digital (130, 216, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 108, 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
(216−86, 216, 202)-Net over F3 — Digital
Digital (130, 216, 202)-net over F3, using
(216−86, 216, 2062)-Net in Base 3 — Upper bound on s
There is no (130, 216, 2063)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 595165 239475 873191 235427 878234 066385 857755 836076 470311 543874 034304 880708 613918 112173 672703 929594 899947 > 3216 [i]