Best Known (168−62, 168, s)-Nets in Base 3
(168−62, 168, 156)-Net over F3 — Constructive and digital
Digital (106, 168, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 84, 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
(168−62, 168, 202)-Net over F3 — Digital
Digital (106, 168, 202)-net over F3, using
(168−62, 168, 2361)-Net in Base 3 — Upper bound on s
There is no (106, 168, 2362)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 144 680680 476734 419986 042294 981001 794783 387326 868741 607285 849014 173941 678534 520985 > 3168 [i]