Best Known (188−72, 188, s)-Nets in Base 3
(188−72, 188, 156)-Net over F3 — Constructive and digital
Digital (116, 188, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 94, 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
(188−72, 188, 201)-Net over F3 — Digital
Digital (116, 188, 201)-net over F3, using
(188−72, 188, 2179)-Net in Base 3 — Upper bound on s
There is no (116, 188, 2180)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 503345 103723 654618 421316 334484 178649 615091 013780 877426 693510 590584 798996 943719 310789 406913 > 3188 [i]