Best Known (232−94, 232, s)-Nets in Base 3
(232−94, 232, 156)-Net over F3 — Constructive and digital
Digital (138, 232, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 116, 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
(232−94, 232, 205)-Net over F3 — Digital
Digital (138, 232, 205)-net over F3, using
(232−94, 232, 2034)-Net in Base 3 — Upper bound on s
There is no (138, 232, 2035)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 495 716439 759424 712801 868756 095224 223671 625317 880545 730607 344869 004552 766201 796187 500916 174313 481202 265328 801395 > 3232 [i]