Best Known (124, 124+80, s)-Nets in Base 3
(124, 124+80, 156)-Net over F3 — Constructive and digital
Digital (124, 204, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 102, 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
(124, 124+80, 201)-Net over F3 — Digital
Digital (124, 204, 201)-net over F3, using
(124, 124+80, 2099)-Net in Base 3 — Upper bound on s
There is no (124, 204, 2100)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 21 857411 815693 485319 006629 655290 060846 812423 661540 843046 296691 294054 433724 017935 759867 524727 018689 > 3204 [i]