Best Known (118, 118+74, s)-Nets in Base 3
(118, 118+74, 156)-Net over F3 — Constructive and digital
Digital (118, 192, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 96, 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
(118, 118+74, 201)-Net over F3 — Digital
Digital (118, 192, 201)-net over F3, using
(118, 118+74, 2155)-Net in Base 3 — Upper bound on s
There is no (118, 192, 2156)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 40 953889 899108 778501 496549 814477 641738 634872 008685 635602 264397 924908 826234 711112 991039 061945 > 3192 [i]