Best Known (228−92, 228, s)-Nets in Base 3
(228−92, 228, 156)-Net over F3 — Constructive and digital
Digital (136, 228, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 114, 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
(228−92, 228, 204)-Net over F3 — Digital
Digital (136, 228, 204)-net over F3, using
(228−92, 228, 2039)-Net in Base 3 — Upper bound on s
There is no (136, 228, 2040)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6 117256 357596 616764 013136 012819 959894 302257 586248 415437 003248 680591 470511 262644 693311 516333 888819 816972 915025 > 3228 [i]