Best Known (122, 122+76, s)-Nets in Base 3
(122, 122+76, 156)-Net over F3 — Constructive and digital
Digital (122, 198, 156)-net over F3, using
- 2 times m-reduction [i] based on digital (122, 200, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 100, 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
- trace code for nets [i] based on digital (22, 100, 78)-net over F9, using
(122, 122+76, 209)-Net over F3 — Digital
Digital (122, 198, 209)-net over F3, using
(122, 122+76, 2263)-Net in Base 3 — Upper bound on s
There is no (122, 198, 2264)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29869 165994 875161 429736 734074 432692 790833 848037 581622 711190 289964 335995 827825 897115 297212 818705 > 3198 [i]