Best Known (123, 123+74, s)-Nets in Base 3
(123, 123+74, 156)-Net over F3 — Constructive and digital
Digital (123, 197, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (123, 202, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 101, 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, 101, 78)-net over F9, using
(123, 123+74, 221)-Net over F3 — Digital
Digital (123, 197, 221)-net over F3, using
(123, 123+74, 2506)-Net in Base 3 — Upper bound on s
There is no (123, 197, 2507)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9976 454239 305812 390783 481088 902372 537145 776980 156485 812922 698438 359710 374351 697157 961238 917263 > 3197 [i]